Class 10 - Chapter 7: Coordinate Geometry

Section A (1 Mark each)

Q1. The distance between the points $(a \cos \theta + b \sin \theta, 0)$ and $(0, a \sin \theta - b \cos \theta)$ is:

(a) $a^2 + b^2$ (b) $a + b$ (c) $\sqrt{a^2 + b^2}$ (d) $\sqrt{a^2 - b^2}$

Q2. If the point $P(2, 1)$ lies on the line segment joining points $A(4, 2)$ and $B(8, 4)$, then:

(a) $AP = \frac{1}{3} AB$ (b) $AP = PB$ (c) $PB = \frac{1}{3} AB$ (d) $AP = \frac{1}{2} AB$

Q3. The perimeter of a triangle with vertices $(0, 4), (0, 0)$ and $(3, 0)$ is:

(a) 5 (b) 12 (c) 11 (d) $7 + \sqrt{5}$

Q4. If $(\frac{a}{3}, 4)$ is the midpoint of the line segment joining the points $P(-6, 5)$ and $R(-2, 3)$, then the value of $a$ is:

(a) $-4$ (b) $-12$ (c) 12 (d) $-6$

Q5. Assertion (A): The point $(0, 2)$ is the point of intersection of the y-axis and the perpendicular bisector of the line segment joining the points $(-1, 1)$ and $(3, 3)$.
Reason (R): Points on the perpendicular bisector of a line segment are equidistant from the endpoints of the segment.

(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)

Q6. Find a relation between $x$ and $y$ such that the point $(x, y)$ is equidistant from the points $(7, 1)$ and $(3, 5)$.

Solve on white paper.

Q7. Check whether $(5, -2), (6, 4)$ and $(7, -2)$ are the vertices of an isosceles triangle.

Solve on white paper.

Q8. If the points $A(6, 1), B(8, 2), C(9, 4)$ and $D(p, 3)$ are the vertices of a parallelogram, taken in order, find the value of $p$.

Solve on white paper.

Section C (3 Marks each)

Q9. Find the coordinates of the points which divide the line segment joining $A(-2, 2)$ and $B(2, 8)$ into four equal parts.

Solve on white paper.

Q10. Find the center of a circle passing through the points $(6, -6), (3, -7)$ and $(3, 3)$.

Solve on white paper.

Section D (Case Study 1 - 4 Marks)

Q11. Case Study: Resident Welfare Association

The Resident Welfare Association of a colony decided to build a triangular park. Three large trees are located at the vertices of the park. On a grid map, the trees are located at $A(3, 1), B(6, 4)$ and $C(8, 1)$.

(i) Find the length of the side AB of the park. [1]

(ii) Find the length of the side BC of the park. [1]

(iii) Is the park in the shape of a right-angled triangle? Justify your answer. [2]

Solve on white paper.

Section E (Case Study 2 - 4 Marks)

Q12. Case Study: GPS Navigation

Aditya starts driving from his house to his office. On a coordinate map, his House is at $H(2, 4)$, his Bank is at $B(5, 8)$, his Daughter's School is at $S(13, 14)$ and his Office is at $O(13, 26)$. He drives from House to Bank, then to School, and finally to Office.

(i) Find the distance between his House and the Bank. [1]

(ii) Find the total distance travelled by Aditya. [2]

(iii) If he had driven directly from his House to the Office, how much distance would he have saved? [1]

Solve on white paper.