CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set D

Case Study Based Questions

I. To conduct sports day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in figure given below. Niharika runs (1/4)^th the distance
AD on the 2nd line and posts a green flag. Preet runs (1/5)^th the distance AD on eighth line and posts a red flag

Answer questions (1) to (5)

Question. Write the coordinates of point N.
(a) (1, 25)
(b) (2, 25)
(c) (4, 25)
(d) (3, 25)
Answer : B

Question. Write the coordinates of point P.
(a) (2, 80)
(b) (8, 2)
(c) (8, 20)
(d) (2, 8)
Answer : C

Question. What is the distance between green and red flags?
(a) √63 m
(b) √26 m
(c) √62 m
(d) √61m
Answer : D

Question. What is the coordinates of R?
(a) (5, 22)
(b) (5, 22.5)
(c) (22.5, 5)
(d) (22, 5)
Answer : B

Question. Distance between Niharika and Rashmi is
(a) 3.90 m
(b) 4.01 m
(c) 3.06 m
(d) 5.10 m
Answer : A

II. In a classroom, 4 friends are seated at the points A, B, C and D as shown is given fig.
Rupa and Rupali walk into the class and after observing for a few minutes Rupa asks Rupali, Some questions which are as follows:

Question. Coordinate of A is
(a) (4, 3)
(b) (3, 0)
(c) (1, 4)
(d) (3, 4)
Answer : D

Question. Coordinate of D is
(a) (6, 1)
(b) (1, 6)
(c) (2, 6)
(d) (6, 2)
Answer : A

Question. Distance AB is
(a) 3+√2
(b) √2
(c) 2√2
(d) 3√2
Answer : D

Question. Diagonal AC is
(a) 3
(b) 4
(c) 6
(d) 5
Answer : C

Question. ABCD is a
(a) rectangle
(b) square
(c) rhombus
(d) trapezium
Answer : B

III. In a classroom, 4 friends are seated at the points A, B, C and D as shown in figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, few questions, which you are required to answer. They are as follows:

Question. What are the coordinates of A and B respectively?
(a) (3, 4) and (6, 7)
(b) (4, 3) and (7, 6)
(c) (–3, 4) and (–6, 7)
(d) (4, –3) and (–7, 6)
Answer : A

Question. What are the coordinates of C and D respectively?
(a) (9, 4) and (6, 1)
(b) (4, 9) and (1, 9)
(c) (–9, –4) and (–6, –1)
(d) (–9, 4) and (–6, 1)
Answer : A

Question. What is the distance between AB and CD?
(a) 4√2 units
(b) 3√2units
(c) 5√2 units
(d) 2√2 units
Answer : B

Question. Distance between BC and AD is
(a) 2√2 units
(b) 4√2 units
(c) 3√2 units
(d) 5√2 units
Answer : C

Question. What is the distance between A and C?
(a) 4 units
(b) 5 units
(c) 8 units
(d) 6 units
Answer : D

1) Show that the points (a, a), (-a, - a) and (- √3a, √3a) are the vertices of an equilateral Δ

2) Show that four points (0,-1), (6, 7), (-2, 3) and (8, 3) are the vertices of a rectangle

3) Prove that (4, -1), (6, 0), (7, 2) and (5, 1) are the vertices of a rhombus. Is it a square?

4) Show that the following points are the vertices of a right angled isosceles triangle: (1, 2), (1, 5) and (4, 2)

5) Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5) (x - y = 2)

6) If the distance of P(x, y) from the points A (3, 6) and B (-3, 4) are equal, prove that 3x + y = 5

7) Find the values of x for which the distance between the points P (2, -3) and Q (x, 5) is 10 units (8 or -4)

8) Given A (-2, 3) and AB = 10 units .If ordinate of B is 9, find abscissa of B (-10, 6)

9) Find the coordinates of the point equidistant from three given points A (5, 1), B (-3, -7) and C (7, -1) (2,-4) 10) If the point p(x, y) is equidistant from the points A (a + b, b - a) and B (a - b, a + b), prove that b x = a y

11) Find the point on y- axis which is equidistant from the point (5, -2) and (-3, 2) (0, -2)

12) Find the point on x- axis which is equidistant from the points (2, -5) and (-2, 9) (-7, 0)

13) If the points A (4, 3), and B(x, 5) are on the circle with the centre. O (2, 3), find the value of x (x=2)

14) The three consecutive vertices of a parallelogram are (-2, 1), (1, 0) and (4, 3). Find the Coordinates of the fourth vertex (1, 4)

15) Find the value of k for which the points (7, -2), (5, 1), and (3, k) are collinear. (k = 4)

16) Find the value of m, for which the points with co-ordinates (3, 5), (m, 6) and [1/2, 15/2] are collinear (m = 2)

17) Find a relation between x and y, if (x, y), (1, 3) and (8, 0) are collinear (3x +7y = 24)

18) If the points (-2, 1), (a, b) and (4,-1) are collinear and a - b = 1, then find the values of a and b (a =1, b = 0)

19) Check whether the points (4, 5), (7, 6) and (6, 3) are collinear.

20) If A (-5, 7), B (-4, -5), C (-1, -6) and D (4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

21) ABCDE is polygon whose vertices are A (-1, 0), B (4, 0), C (4, 4), D (0, 7) and E (-6, 2). Find the area of the polygon

22) Using A (4, -6), B (3, -2) and C (5, 2), verify that a median of the ΔABC divides it into two triangles of equal areas

23) The coordinates of A, B, C are (3, 4), (5, 2), (x, y) respectively. If area of ΔABC = 3, show that x + y = 10

24) The coordinates of the vertices of ΔABC are A (4, 1), B (-3, 2) and C (0, k).Given that the area of ΔABC is 12 unit2, Find the Value of k (k = - 13/ 7)

25) Find the ratio in which the point (2, y) divides the line segment joining the points A (-2, 2) and B (3, 7) (4: 1)

26) If P divides the join of A (-2, -2) and B (2, -4) such that AP/AB = 3/7, find the coordinates of P (-2/7, -20/7)

27) Find the ratio in which the line 2x + y – 5 = 0 divides the line segment joining A (2,-3) and B (3, 9) (2:5)

28) Determine the ratio in which the line 3x + 4y – 9 = 0 divides the line segment joining the points (1, 3) and (2, 7) (k = - 6/25)

29) Find the length of medians of triangle whose vertices are A (-1, 3), B (1, -1), and C (5, 1)

30) If the midpoint of of the segment joining A (a, b +1), and B (a +1, b +2) is C (3/2, 5/2) Find a and b (a=1, b=1)

31 The coordinates of one end point of a diameter of a circle are (4, -1) and the coordinates of the centre of the circle are (1, -3)

Find the coordinates of the other end of the diameter (-2, -5)

32) If P(x, y) is any point on the line joining the points A (a, 0), B (0, b), then show that x + y a b

33) The centre of a circle is (2a – 1, 7) and it passes through the point (-3, -1). If the diameter of the circle is 20 units, then find

the value of a (-4, 2)

34) Determine the value of a if AB = BC, where A, B, C are the points (-5, 1), (0, 5) and (a, 1) respectively (±5)

35) A (5, -1), B (-1, 8) and C (-3, -2) are the vertices of triangle ABC. E and F are the midpoints of the sides AB and AC Respectively.Show that EF = ½ BC

PREPARED BY MAHABOOB PASHA ] X – X BOYS

Please click the below link to access CBSE Class 10 Mathematics Worksheet - Coordinate Geometry (4)