CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set 02

Question. The distance of the point P (–3, –4) from the x-axis (in units) is
(a) 3
(b) –3
(c) 4
(d) 5
Answer : C

Question. The distance of a point from the origin is
(a) x² + y²
(b) x² – y²
(c) √x² + y²
(d) None of these
Answer : C

Question. The distance between the points (3, –2) and (–3, 2) is
(a) √52 units
(b) 4√10 units
(c) 2√10 units
(d) 40 units
Answer : C

Question. If points (a, 0), (0, b) and (1, 1) are collinear, then the value of 1/a + 1/b is
(a) 1
(b) 2
(c) 5
(d) 9
Answer : A

Question. If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?
(a) k = 4
(b) k = –4
(c) k = ± 4
(d) None of these
Answer : C

Question. The distance of the point P (3, –4) from the origin is
(a) 7 units
(b) 5 units
(c) 4 units
(d) 3 units
Answer : B

Question. The distance between the points - (5/8, 2) and (2/5, 2) is
(a) 0 units
(b) 1 unit
(c) 2 units
(d) 5 units
Answer : C

Question. The perpendicular distance of A(5, 12) from the y-axis is
(a) 4
(b) 5
(c) 7
(d) 8
Answer : B

Question. The points (a, a), (–a, –a) and (−√3a, √3a) are the vertices of a/an
(a) Equilateral triangle
(b) Isosceles triangle
(c) Scalene triangle
(d) None of these
Answer : A

Question. If the distance of P(x, y) from A(5, 1) and B(–1, 5) are equal, then 3x equals
(a) y
(b) y/2
(c) 2y
(d) 2/y
Answer : C

Question. If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), the value of p is
(a) 5 units
(b) 8 units
(c) √10 units
(d) None of these
Answer : C

Question. The value(s) of x, if the distance between the points A(0, 0) and B(x, – 4) is 5 units, is
(a) ± 2
(b) ± 3
(c) ± 4
(d) ± 5
Answer : B

Question. The distance between (√2 + 1, 2) and (1, 2 − √2) is
(a) 2
(b) 3
(c) 11
(d) 17
Answer : A

Question. The value of k for which the point (0, 2) is equidistant from two points (3, k) and (k, 5) is
(a) 1
(b) 2
(c) 5
(d) 9
Answer : A

Question. Points A(2, –1), B(3, 4), C(–2, 3), D(–3, –2) are the vertices of a:
(a) Rectangle
(b) Square
(c) Rhombus
(d) None of these
Answer : C

Question. The value(s) of y, if the distance between the points (2, y) and (– 4, 3) is 10, is
(a) 11
(b) –5
(c) Both (a) and (b)
(d) None of these
Answer : C

Question. The point on x-axis which is equidistant from the points (2, –2) and (–4, 2) is
(a) (1, 0)
(b) (2, 0)
(c) (0, 2)
(d) (–1, 0)
Answer : A

B. Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R).
Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate on the point on y-axis is zero.
Answer : A

Question. Assertion (A): The value of y is 6, for which the distance between the points P(2, –3) and Q(10, y) is 10.
Reason (R): Distance between two given points A (x₁, y₁) and B (x₂, y₂) is given by

Answer : D

Case Study Based Questions

I. Class X students of a secondary school in Krishnagar have been allotted a rectangular plot of a land for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

Considering A as origin, answer question (1) to (5).

Question. Considering A as the origin, what are the coordinates of A?
(a) (0, 1)
(b) (1, 0)
(c) (0, 0)
(d) (–1, –1)
Answer : C

Question. What are the coordinates of P?
(a) (4, 6)
(b) (6, 4)
(c) (4, 5)
(d) (5, 4)
Answer : A

Question. What are the coordinates of R?
(a) (6, 5)
(b) (5, 6)
(c) (6, 0)
(d) (7, 4)
Answer :A

Question. What are the coordinates of D?
(a) (16, 0)
(b) (0, 0)
(c) (0, 16)
(d) (16, 1)
Answer : A

Question. What are the coordinates of P if D is taken as the origin?
(a) (12, 2)
(b) (–12, 6)
(c) (12, 3)
(d) (6, 10)
Answer : B
 

II.

In a classroom, 4 friends have decided to seat at the points A, B, C and D as shown in fig. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli some questions which are as follows:

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

Question. What is the coordinate of C and D?
(a) C(4, 9), D(1, 6)
(b) C(9, 4), D(6, 1)
(c) C(–9, –4), D(–6, –1)
(d) C(9, –4), D(6, –1)
Answer : B

Question. What is the distance between AB?
(a) 2
(b) 3
(c) 2 3
(d) 3 2
Answer : D

Question. What is the distance between AC?
(a) 6
(b) 4
(c) 8
(d) 10
Answer : A

Question. What is the distance between BD?
(a) 4
(b) 6
(c) 8
(d) 10
Answer : B

Please refer to attached file for CBSE Class 10 Mathematics Worksheet - Coordinate Geometry (2)