CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set B

CASE STUDY - 1

Rajeev went out from his house to reach the office. But he had to get some work done before going to the office. So, he first of all went to the bank first, from there he went to his son's school, and then reaches to office. The position of home, school, bank and office on coordinate axis is shown in the following figure:
Now, answer the following questions:

(i) If Rajeev goes directly from bank to his office, how much distance he would travel?
(a) 2√97 units
(b) 9√17 units
(c) 7√7 units
(d) 7√45 units
Answer : A

(ii) How much distance he will travel, if goes directly from home to the office?
(a) 15√7 units
(b) 10 units
(c) 14√3 units
(d) 11√5 units
Answer : D

(iii) If at the mid-point of the bank and school, there is a park, what are the coordinates of the park?
(a) (13, 14)
(b) (9,11)
(c) (-5, 10)
(d) (10, 12)
Answer : B

(iv) Find the distance of the point (-6, 8) from the origin.
(a) 8 units
(b) 10 units
(c) 11 units
(d) 9 units
Answer : B

Very Short Answer type Questions

Question. Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.
Answer : y = 3 or y = -9

Question. If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5), then find the coordinates of the other two vertices.
Answer : (1,-12) and (5,-10)

Question. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order find x and y.
Answer : x = 6 and y = 3

Question. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.
Answer : 24 square units

Question. Find the point on the x-axis which is equidistant from (2, -5) and (- 2, 9).
Answer : (-7,0)

Question. Find the ratio in which the line segment joining A (1, – 5) and B (- 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
Answer : k =1 and (-3/2, 0)

Question. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).
Answer : (2, -5/3) and (0, -7/3)

Question. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).
Answer : 3x + y - 5 = 0

Question. Find the type of quadrilateral formed by the points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) and justify your answer.
Answer : Square

Question. Find the centre of the circle passing through A (6, -6), B (3, -7) and C (3, -3).
Answer : (4,-5)

Coordinate Geometry

Question. Determine (i) Abscissa (ii) ordinate (iii) Co-ordinates of point P given in the following figure.

Question. Draw a rectangle PQRS in which vertices P, Q,R and S are (1, 4), (–5, 4), (–5, –3) and (1, – 3) respectively.

Answer : Plot the point P by taking its abscissa 1 and ordinate – 4.

Similarly, plot the points Q, R and S taking abscissa as –5, –5 and 1 and ordinates as 4, – 3 and –3 respectively.

Join the points PQR and S. PQRS is the required rectangle.

Please click on below link to download CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set B