Class 10 - Chapter 7: Coordinate Geometry

Section A (1 Mark each)

Q1. The coordinates of the point which divides the line segment joining the points $(4, -3)$ and $(8, 5)$ in the ratio $3:1$ internally is:

(a) $(7, 3)$ (b) $(3, 7)$ (c) $(4, 3)$ (d) $(7, 4)$

Q2. If the point $P(k, 0)$ divides the line segment joining the points $A(2, -2)$ and $B(-7, 4)$ in the ratio $1:2$, then the value of $k$ is:

(a) 1 (b) $-1$ (c) 2 (d) $-2$

Q3. The centroid of the triangle whose vertices are $(3, -7), (-8, 6)$ and $(5, 10)$ is:

(a) $(0, 9)$ (b) $(0, 3)$ (c) $(1, 3)$ (d) $(3, 3)$

Q4. Assertion (A): The point $P(-4, 6)$ divides the line segment joining the points $A(-6, 10)$ and $B(3, -8)$ in the ratio $2:7$.
Reason (R): The coordinates of the point $P(x, y)$ which divides the line segment joining the points $A(x_1, y_1)$ and $B(x_2, y_2)$ in the ratio $m_1:m_2$ are $(\frac{m_1x_2+m_2x_1}{m_1+m_2}, \frac{m_1y_2+m_2y_1}{m_1+m_2})$.

(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 coordinates of the midpoint of the line segment joining the points $(-5, 7)$ and $(-1, 3)$.

Solve on white paper.

Q6. Find the ratio in which the line segment joining the points $(-3, 10)$ and $(6, -8)$ is divided by $(-1, 6)$.

Solve on white paper.

Q7. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is $(2, -3)$ and B is $(1, 4)$.

Solve on white paper.

Section C (3 Marks each)

Q8. Find the coordinates of the points of trisection of the line segment joining $(2, -2)$ and $(-7, 4)$.

Solve on white paper.

Q9. Find the ratio in which the y-axis divides the line segment joining the points $(5, -6)$ and $(-1, -4)$. Also find the point of intersection.

Solve on white paper.

Section D (5 Marks)

Q10. If $A(-2, -2)$ and $B(2, -4)$ are two points, find the coordinates of $P$ such that $AP = \frac{3}{7} AB$ and $P$ lies on the line segment $AB$.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study: Sports Day

In a rectangular school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD. Niharika runs $\frac{1}{4}$th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$th the distance AD on the 8th line and posts a red flag.

(i) Find the coordinates of the green flag. [1]

(ii) Find the coordinates of the red flag. [1]

(iii) Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags. Where should she post her flag? [2]

Solve on white paper.