Class 10 - Chapter 7: Coordinate Geometry

Section A (1 Mark each)

Q1. The distance of the point $P(2, 3)$ from the x-axis is:

(a) 2 (b) 3 (c) 1 (d) 5

Q2. The distance of the point $P(-6, 8)$ from the origin is:

(a) 8 (b) $2\sqrt{7}$ (c) 10 (d) 6

Q3. The midpoint of the line segment joining the points $A(-2, 8)$ and $B(-6, -4)$ is:

(a) $(-4, -6)$ (b) $(2, 6)$ (c) $(-4, 2)$ (d) $(4, 2)$

Q4. Assertion (A): The point $(0, 4)$ lies on the y-axis.
Reason (R): The x-coordinate of a point on the y-axis is zero.

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Section B (2 Marks each)

Q5. Find the value of $y$ for which the distance between the points $P(2, -3)$ and $Q(10, y)$ is 10 units.

Solve on white paper.

Q6. Find the ratio in which the y-axis divides the line segment joining the points $(5, -6)$ and $(-1, -4)$.

Solve on white paper.

Q7. If $(1, 2), (4, y), (x, 6)$ and $(3, 5)$ are the vertices of a parallelogram taken in order, find $x$ and $y$.

Solve on white paper.

Section C (3 Marks each)

Q8. Find the coordinates of the points of trisection of the line segment joining $(4, -1)$ and $(-2, -3)$.

Solve on white paper.

Q9. Find the point on the x-axis which is equidistant from $(2, -5)$ and $(-2, 9)$.

Solve on white paper.

Section D (5 Marks)

Q10. Find the area of a rhombus if its vertices are $(3, 0), (4, 5), (-1, 4)$ and $(-2, -1)$ taken in order.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: Classroom Seating

In a classroom, 4 friends are seated at points A, B, C and D as shown in a grid. The coordinates are $A(3, 4)$, $B(6, 7)$, $C(9, 4)$ and $D(6, 1)$.

(i) Find the distance AB. [1]

(ii) Find the distance BC. [1]

(iii) Check if ABCD is a square. Justify your answer. [2]

Solve on white paper.