CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set E

Case Study Based Questions

I. Student of a school are standing in rows and columns in a playground for a drill practice.
A, B, C, D are the positions of four students as shown in the figure

Question. The coordinates of A and B are respectively
(a) (3, 5) and (7, 9)
(b) (5, 3) and (9, 7)
(c) (–3, –5) and (7, 9)
(d) (3, 5) and (–7, –9)
Answer : A

Question. The coordinates of the points C and D are respectively
(a) (5, 11) and (1, 7)
(b) (11, 5) and (7, 1)
(c) (–5, –11) and (–1, –7)
(d) (5, 11) and (–1, –7)
Answer : B

Question. The distance between A and B is
(a) 4√2 units
(b) 3√2 units
(c) 5√2 units
(d) 2√2 units
Answer : A

Question. The distance between A and C is
(a) 8 units
(b) 8√2 units
(c) 5√2 units
(d) 3√2 units
Answer : A

Question. The coordinates of the point which is equidistant from each of the four students A, B, C and D are
(a) (5, 7)
(b) (–5, –7)
(c) (–7, –5)
(d) (7, 5)
Answer : D

II. Three friends are playing in a ground to form a triangle. They are standing at the vertex of the triangle having coordinates A(2a, 4a), B(2a, 6a) and C(2a + a√3 , 5a). Teacher wants to check the some measurements of the triangle and ask few questions. Answer them.

Question. Length of AB is
(a) 2a
(b) 4a
(c) 8a
(d) 6a
Answer : A

Question. Length between the points B and C is
(a) a
(b) 2a
(c) 4a
(d) 6a
Answer : B

Question. Length between the point A and C is
(a) a
(b) 2a
(c) 3a
(d) 4a
Answer : B

Question. Mid-point of AB is
(a) (2a, 5a)
(b) (4a, 5a)
(c) (2a, 3a)
(d) (5a, 4a)
Answer : A

Question. Height of triangle =
(a) √2a
(b) 3a
(c) √3a
(d) √5a
Answer : C
 

III. Kartikeya starts walking from his house to office. Instead of going to the office directly, he goes to the bank first, from there to his daughter’s school and then reaches the office. Assuming that all distances covered are in straight lines and if the coordinates of house at (2, 4), bank at (5, 8), school at (13, 14) and office (13, 26) are represented in km. Then find answer from question (1) to question (5).

Question. Total distance covered by Kartikeya is
(a) 27 km
(b) 24 km
(c) 30 km
(d) 18 km
Answer : A

Question. Extra distance travelled by Kartikeya in reaching his office is
(a) 1.5 km
(b) 3.7 km
(c) 2.41 km
(d) 4 km
Answer : C

Question. Distance travelled by Kartikeya in reaching his daughter’s school is
(a) 14 km
(b) 20 km
(c) 15 km
(d) 10 km
Answer : A

Question. The shortest distance between his house and the office is
(a) 12.53 km
(b) 20.53 km
(c) 14.53 km
(d) 24.59 km
Answer : D

Question. The distance between his daughter’s school and his office is
(a) 10 km
(b) 12 km
(c) 16 km
(d) 18 km
Answer : B

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 (5)