Q1.
While writing the coordinates of a point, which coordinate comes first?
Q2.
The two points which lies on the y-axis and which are at equal distances from the origin are:
Q3.
The coordinates of a point are (x, y) and it lies in the 3rd quadrant. Which of the following is true?
Q4.
The two quadrants where the value of abscissa are negative are:
Q5.
The distance of a point (4, 6) from the y-axis is
Q6.
Which of the following correctly represents the quadrants containing the points (−5,4) and (4,−5), respectively?
Q7.
The point (-7, 0) lies on
Q8.
If x-coordinate of a point is zero, then it always lies on
Q9.
What are the coordinates of the point which lies on neither axes at a distance of 2 units from the x-axis and 7 units from the y-axis?
(7, 2)
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Q10.
In which quadrants do the points lie when the abscissa and ordinate have different signs?
II and IV quadrants
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Q11.
The distance of the given Point (-3, 2) from the x-axis is
Q12.
Based on the given coordinate graph, which ordered pairs correspond to points P and Q, respectively?
Q13.
If y-coordinate of a point is zero, then where will this point lie in the coordinate plane?
on the x- axis
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Q14.
Meren is standing on the school playground shown on the coordinate plane. What are his coordinates?
(2, 3)
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Q15.
The point (-4, 5) lies in
Q16.
From the graph, find the points identified by the coordinates (-6, -2) and (0, 3).
Q and N
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Q17.
In the Cartesian Plane, what is the name of the point where the two lines intersect?
Q18.
The name of each part of the plane formed by the two lines is
Q19.
The vertical line drawn to determine the position of a point on the Cartesian Plane is called
Q20.
Ordinate of all points on the x-axis is
Q21.
What are the coordinates of the point which lies on the x-axis with abscissa -3?
(-3, 0)
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Q22.
What are the coordinates of the point which lies on the y-axis with ordinate 5?
(0, 5)
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Q23.
In the figure, the centre of the circle lies in the origin. If the radius of the circle is 5 units, then what are the coordinates of the point A?
(0, -5)
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Q24.
In the given figure, a quadrilateral is formed by joining the points P, Q, R, and S. What is the name of this quadrilateral?
Trapezium
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Q25.
Q is a point on the y-axis at a distance of 7 units from the x-axis lying below the x-axis. The coordinates of the point Q are
Q26.
If (x, y) = (y, x), which of the following is true?
Q27.
In which quadrants do the points (−5,2) and (2,−5) lie?
2nd and 4th quadrants, respectively.
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Q28.
Without plotting the points P(−1,1), Q(3,−4), R(1,−1), S(−2,−3), and T(−4,4) on a graph, determine which of the following points lie in the fourth quadrant.
Q29.
If the coordinates of the two points are P(-2, 3) and Q(- 3, 5), then (Abscissa of P) – (Abscissa of Q) is
Q30.
The coordinates of the origin are
Q31.
Signs of the abscissa and ordinate of a point in the second quadrant are respectively:
Q32.
Signs of the abscissa and ordinate of a point in the fourth quadrant are respectively:
Q33.
Based on the provided Cartesian plane, what are the coordinates of points P and S?
(1, 4) and (-2, -4)
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Q34.
In the given figure, LM is a line parallel to the y-axis at a distance of 3 units. What is the difference between the abscissae of the points L and M?
0
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Q35.
Which of the following point lies on y-axis?
Q36.
The coordinates of a point which lies on the x-axis at a distance of 7 units from the y-axis are (7, 0). What will be the coordinates if it lies on the y-axis at a distance of –7 units from the x-axis?
(0, -7)
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Q37.
Observe the Cartesian plane and name the points whose abscissa is 0.
A and L
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Q38.
The point (–4, –3) represents which of the following?
Q39.
A point is at a distance of -3 units from the x-axis and +5 units from the y-axis. Which of the following is the coordinates of the point?
Q40.
The coordinates of a point are (2,7). What is its distance from the y-axis?
2
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Q41.
Which of the following point is on -ve y-axis?
Q42.
A point lies on the y-axis and its ordinate is -3. What are the coordinates of the point?
(0, -3)
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Q43.
In which quadrants are the signs of both the abscissa and the ordinate the same?
1st and 3rd quadrants
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Q44.
The perpendicular distance of a point from the x-axis is 6 and that from the y-axis is 2. What are the coordinates of the point?
(2, 6)
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Q45.
Find the coordinates of the point whose ordinate is 2 and lies on the y-axis?
(0, 2)
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Q46.
The perpendicular bisector of a line segment AB passes through the origin. If the coordinates of A are (-2, 0), then what will be the coordinates of B?
(2, 0)
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Q47.
Observe the Cartesian plane and identify the points whose ordinate is zero.
I and G
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Q48.
In the given figure, PQ is a line parallel to the x-axis at a distance of 4 units. What is the difference between the ordinates of points P and Q?
0
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Q49.
Which one of the following points does not lie on the x-axis?
Q50.
If the coordinates of two points are A(-7,9) and B(3,4), then find the value of (ordinate of A) – (ordinate of B).
5
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Q51.
If (\( x^2 \), y + 1) = (5, \(\sqrt{5} \)), then what is the value of y?
\(\sqrt{5} \) −1
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Q52.
In the given figure, ABCD is a square of side '2a'. Taking AB and AD as the x-axis and y-axis respectively, find the coordinates of point C.
(2a, 2a)
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Q53.
From the given figure, determine the coordinates of points A and B.
(−3, 4) and (4,−3)
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Q54.
In the given coordinate plane, three vertices of a rectangle are shown. What are the coordinates of the fourth vertex?
(3, 5)
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Q55.
The coordinates of two points A and B are respectively (4, 3) and (4, -5). Find the coordinates of the point at which the line segment AB meets the x-axis.
(4, 0)
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Q56.
The coordinates of two points are P(-2, 3) and Q(-3, 5). Find
[(abscissa of P) – (abscissa of Q)] + [(ordinate of Q) – (ordinate of P)].
3
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Q57.
Find the coordinates of a point in the first quadrant that does not lie on either axis and is 2 units away from the y-axis and 7 units away from the x-axis.
(2, 7)
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Q58.
The ordinates of the points P and P' are of equal magnitudes but of opposite signs. If the point P lies in the second quadrant, then in which the point P' lies?
3rd Quadrant
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Q59.
What are the coordinates of a point which is at a distance of 4 units to the left of y-axis and 4 units above the x-axis?
(-4, 4)
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Q60.
A graph shows a straight line passing through the points (-3, 6) and (3, 2). Based on the visual representation, find the coordinates of the points where the line intersects the x-axis and the y-axis.
x-axis intersection: (6, 0), y-axis intersection: (0, 4)
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Q61.
If a point (x, y) lies in the second quadrant, then the nature of x and y are
Q62.
If (x+4, 2) = (5, y−2), then find the value of (x, y).
(1, 4)
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Q63.
The coordinates of points P and Q are (−5, 3) and (−5, m) respectively, and the sum of the abscissa and ordinate of point P is equal to that of point Q. Find the value of m.
m = 3
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Q64.
From the point P(−6, 2), perpendiculars PM and PN are drawn to the x-axis and y-axis respectively. What are the coordinates of M and N?
M(-6, 0) and N(0, 2)
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Q65.
What is the general form of the coordinates of a point lying on the x-axis?
(x, 0)
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Q66.
What is the distance of a point from the y-axis called?
x-coordinate or abscissa
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Q67.
If the ordinate of a point is 5 and its abscissa is −3, in which quadrant does the point lie?
Q68.
Point (–1, 0) lies in the:
Q69.
A point on the x-axis is at a distance of 5 units from the y-axis in the negative direction. Find the coordinates of the point.
(-5, 0)
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Q70.
What is the general form of the coordinates of a lying on the y-axis?
(0, y)
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Q71.
What is the distance of a point from the x-axis called?
y-coordinate or ordinate
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Q72.
Signs of the abscissa and ordinate of a point in the third quadrant are respectively:
Q73.
The perpendicular distances of the point A(m, 2n) from both the x-axis and the y-axis are 6 units each. Given that m < 0 and n > 0, then what are the coordinates of point B(n+1, m)?
Coordinates of point B(n+1, m) are (4, -6)
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Q74.
Which of the following points does not lie in III quadrant ?
Q75.
The given points are (2, –1), (6, –5), and (–3, –2). Which of the following statements is true?
Q76.
If the coordinates of the two points are P(–5, 3) and Q(8, –9), then what is the value of (ordinate of Q) – (ordinate of P)?
– 12
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Q77.
If the points P(5, 1), Q(0, 2), R(3, 0), and S(–1, 0) are plotted on a graph paper, which point lies on the y-axis?
Q
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Q78.
Four children—Deepak, Ashok, Arjun, and Deepa—were playing with their footballs in a square park ABCD. The positions of their balls are shown in the given figure. By joining the positions of the four balls in order, identify the quadrilateral formed. Also, find its area.
The quadrilateral formed is an isosceles trapezium, and its area is 42 square units.
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Q79.
As part of an anti-smoking awareness campaign, students prepared a "NO SMOKING" banner in the shape of a triangle, as shown in the figure. Find the area of triangle PQR.
21 sq. units
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Q80.
Point A is chosen on y-axis in such a way that ΔABC is an equilateral triangle. The base BC of the ΔABC is 6 units as shown in the figure. Find the coordinates of B and C.
B(−3, 0), C(3 ,0).
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Q81.
Observe the given graph and find the perpendicular distance of point E from the y-axis.
10 units
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Q82.
P(3,2) and Q(7,7) are two points. Perpendiculars are drawn to the x-axis from P and Q meeting the x-axis at L and M respectively.
i) Find the coordinates of L and M.
ii)Find the length of LM.
(i) L (3, 0) Coordinates of M (7, 0) (ii) Length of LM = 4 units
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Q83.
The abscissa of a point is 2 and its ordinate is −5. What are the coordinates of the point? Also, in which quadrant does the point lie?
Coordinates are (2, -5). The point point lies in the fourth quadrant.
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Q84.
What are the coordinates of the point that lies on both the x-axis and the y-axis?
(0, 0)
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Q85.
In the given Cartesian coordinate system, a triangle ABC and a rectangle DEFG are plotted. Based on the graph, which of the following represents the coordinates of the vertices of triangle ABC?
Q86.
What is the intersection point of the line x=5 with x-axis?
(5, 0)
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Q87.
Vivek wants to purchase a painting for drawing room. First of all, he puts a grid on the wall so that he could hang a painting on that area. The corner points of the grid are A (2, 4); B (6, 4); C (6, 8) and D (2, 8).
what is the area of the painting?
16 sq units
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Q88.
A student marks the points (4, 0), (0, 2), (–4, 0), and (0, –2) on a graph paper and joins them using line segments. What type of quadrilateral is formed? Also, find its area.
Name of the quadrilateral is Rhombus; Area of Rhombus is 16 sq. units
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Q89.
In the given figure , POQ is a triangle with coordinate of P and O as (\(\sqrt{13} \) , 0) and (0, 0) respectively. If PQ = 7, find the coordinates of Q.
( 0, 6)
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Q90.
A triangle with vertices (0, 0), (5, 0), and (5, 4) is shown in the given graph. Find the area of the triangle.
10 sq. units
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Q91.
Sunep wants to decorate his drawing room by placing a painting on a marked section of the wall. To plan the placement, he draws a grid on the wall. The corner points of this grid are A(2, 4), B(6, 4), C(6, 8), and D(2, 8). what is the perimeter of the painting?
16 sq. units
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Q92.
A man travels daily between his home (H), his son's school (S), and his office (O). The locations of these places are represented on a Cartesian plane, where each unit on both axes represents 1 km. What is the distance between home and office?
5 km
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Q93.
If (x + 2, 4) = (5, y – 2), then which of the following represents the ordered pair (x, y)?
Q94.
On Annual Sports Day, parallel lines 1 m apart were marked on a rectangular playground. Eighty cones were placed 1 m apart along PY, as shown in the figure. Ankit ran \( \frac{1}{4} \) of the distance PY on the 3rd line and placed a yellow flag, while Ankur ran \( \frac{1}{5} \) of the distance PY on the 7th line and placed a blue flag. What are the coordinates of the yellow and blue flags?
Yellow Flag:(3, 20) ; Blue Flag:(7, 16)
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Q95.
A circular clock is drawn on a Cartesian plane, as shown in the figure. The boundary of the clock intersects the coordinate axes at a distance of \( \frac{4}{3} \) units from the origin. Based on the figure, find the area of the circle?
\( \frac{16}{9} \) π sq. units
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Q96.
What is required to represent the exact position of an object on a plane?
Q97.
The idea of locating a point using two perpendicular lines led to the development of which branch of mathematics?
Q98.
Who is credited with the development of Coordinate Geometry?
Q99.
Observe the classroom seating plan, where columns represent the x-axis and rows represent the y-axis. Sonia’s desk is marked as ‘S’. What are Sonia’s coordinates?
(4,1)
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Q100.
How many independent pieces of information are required to determine the position of the dot shown in the figure? What are they?
Two; The horizontal distance from the y-axis and the vertical distance from the x-axis .
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Q101.
A student marks a dot on a sheet of paper such that it is 5 cm from the left edge and 9 cm from the bottom edge. Taking the left edge as the Y-axis and the bottom edge as the X-axis, which of the following represents the coordinates of the dot?
Q102.
The given figure shows the coordinates of a table lamp as (15, 25). Taking the breadth of the table as the X-axis and the length as the Y-axis, what does the number 15 represent in terms of its position on the table?
Distance of the lamp from the Y-axis (i.e., x-coordinate or abscissa).
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Q103.
A city has two main roads intersecting at the center—one running North–South and the other East–West. All other streets run parallel to these main roads and are 200 m apart. There are 5 streets in each direction. How many cross-streets are formed in the city model?
25 cross-streets
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Q104.
Rahul notes the position of his lamp as (25, 30) on a coordinate plane. While cleaning, he moves it 10 units to the right and 5 units downward. What will be the new coordinates of the lamp?
(35, 25)
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Q105.
A city layout shows two main roads crossing at the center—one running North–South and the other East–West. All other streets are parallel to these main roads and are 200 m apart, with 5 streets in each direction. If a shop is located at every intersection along Street 2 (running North–South), how many shops are there on that street?
5 shops
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Q106.
A table lamp is located at (15, 25), where breadth is along the X-axis and length along the Y-axis. If the axes are interchanged, what will be the new coordinates of the lamp?
(25, 15)
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Q107.
During a Maths activity, four students stood at points A(2,2), B(6,2), C(6,5), and D(2,5), forming a rectangular arrangement as shown in the figure. The teacher then shifted the entire rectangular arrangement 3 units to the right. Based on the given information, which one of the following represents the new coordinates of all four vertices?
Q108.
A communication tower is installed at Q(0,2), and an underground sensor at R(0,−2). A relay station P is located on the positive x-axis at a distance of 6 units from the y-axis as shown in the figure.
Which of the following are the coordinates of the relay station P?
Q109.
A straight line passes through the points P(−5, 4) and Q(5, 4). What are the coordinates of the point where the line intersects the y-axis?
(0, 4)
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Q110.
In the given graph, the coordinates of three vertices P,Q, and R of a quadrilateral are given. Find the coordinates of the fourth vertex S and name the quadrilateral so obtained.
S(2, 2); Trapezium
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Q111.
In the provided figure, the line segment CD has been reflected across the y-axis to create the image C'D'. What are the coordinates of C' and D'?
C'(-2, 7); D'(-9, -5)
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Q112.
In the given figure, △ABC with vertices A(2,8), B(6,4), and C(4,−2) is reflected across the x-axis. Which of the following are the coordinates of the image?
Q113.
If the point (−4, 6) is reflected across the y-axis, what are the coordinates of the new point?
(4, 6)
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Q114.
If the point (2, 3) is reflected across the x-axis, what are the coordinates of the new point?
(2, −3)
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Q115.
A point is reflected across the y-axis. Which of the following is true?
Q116.
A point is reflected across the x-axis. Which of the following is true?
Q117.
Students are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in the figure. What are the coordinates of A and B respectively?
A(3, 5); B(7, 9)
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Q118.
In the following question, a statement of Assertion (A) is followed by a statement of Reason (R).
Assertion (A): The abscissa of the point (5, 2) is 5.
Reason (R): The perpendicular distance of a point from the y-axis is called its abscissa.
Choose the correct answer from the options given below:
Q119.
The Class IX students of a secondary school were given a rectangular plot of land for their gardening activity. Gulmohar saplings were planted along the boundary of the plot at intervals of 1 metre from each other. A lawn PQRS is situated inside the ground, as shown in the figure. What are the coordinates of C, taking A as origin?
C(10, 6)
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Q120.
In the figure, ABCD is a rectangle in which AB=8 units and BC=6 units. If P, Q, R, and S are the midpoints of AB, BC, CD, and DA respectively. Find the coordinates of A and C.
A(-4, -3) and C(4, 3)
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Q121.
What is the area of the triangle formed by joining the points (8, 0), (12, 0), and (12, 4)?
8 sq. units
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Q122.
In the following question, a statement of Assertion (A) is followed by a statement of Reason (R).
Assertion (A): Point (4, -2) lies in IV quadrant.
Reason (R): The perpendicular distance of a point from y-axis is called its abscissa.
Choose the correct answer from the options given below:
Q123.
The figure shows an equilateral triangle OAB with each side equal to 2a units. Find the coordinates of the vertices O and B from the figure.
O(0,0); B(2a,0)
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Q124.
Observe the given figure. Imagine a rectangular "Security Zone" is drawn such that its sides are parallel to the X and Y axes. The Hospital (0,0) is one corner, and the Library (6,2) is the opposite corner of the rectangle. What are the coordinates of the other two corners of the Security Zone? Also, determine the perimeter of the Security Zone.
(6,0) and (0,2). The perimeter = 16 units
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Q125.
If the coordinates of two points P and Q are (2, –3) and (–6, 5), then find the value of (x-coordinate of P) – (x-coordinate of Q)?
8
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Q126.
ABC is an equilateral triangle as shown in the figure. If BC=6 units, what are the coordinates of vertex A?
(0, 3 \(\sqrt{3} \))
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Q127.
The given graph represents the locations of four important places in a town: a Hospital, a School, a Police Station, and a Library.
Based on the graph, answer the following question.
(i) A health awareness program is to be conducted by the Hospital at the School. What are the coordinates of both locations?
(ii) In which quadrant is the School located?
(i) Hospital (0,0), School (2,3) (ii) First Quadrant
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Q128.
A rectangular plot ABCD is shown on the coordinate graph. Within this plot, a square lawn PQRS has been laid out. Calculate the area of the lawn PQRS.
34 sq. units
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Q129.
The image shows the positions of bears on a coordinate grid, with the origin representing the ranger’s control room and Roads X and Y pass through this point. Each unit on the grid represents 1 km. Based on the given information, answer the following questions
A tiger is spotted at the point (11, 4). Which bear is nearest to the tiger, and how far away is it?
.
Bear 389; 2 km
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Q130.
Limasen and Yanithung live in Landmark Colony. Their school is situated at the origin O. Limasen's house is represented by point A, Yanithung's house by point B, and the children's park by point C. Based on the above information, which of the following is true?
