# Important Questions Exercise 7.1 Class 10 Maths Chapter 7 Coordinate Geometry

### Important Questions Exercise 7.1 Class 10 Maths Chapter 7 Coordinate Geometry

Students gearing up for the 2022-23 board exams are strongly encouraged to engage in rigorous practice with these crucial Coordinate Geometry questions. This dedicated practice will enhance their chances of securing top scores in the upcoming Mathematics examination. By tackling these questions, students will acquire valuable problem-solving skills that can be applied to any challenge presented in this chapter during the exam. Furthermore, working through these questions serves as an effective revision tool, significantly boosting students’ confidence levels.

#### Important Questions Assignment Exercise 7.1

**Question 1.** Find the distance of the point (-3, 4) from the x-axis. (CBSE 2012)

**Question 2.** If the points A(x, 2), B(-3, 4) and C(7, -5) are collinear, then find the value of x. (CBSE 2014)

**Question 3. **ABCD is a rectangle whose three vertices are B(4, 0), C(4, 3) and D(0, 3). Calculate the length of one of its diagonals. (CBSE 2014)

**Question 4.** In the figure, calculate the area of triangle ABC (in sq. units). (CBSE 2013)

**Question 5.** Find a relation between x and y such that the point P(x, y) is equidistant from the points A (2, 5) and B (-3, 7). (CBSE 2011)

**Question 6**. If the distance between the points (4, k) and (1,0) is 5, then what can be the possible values of it? [CBSE 2017]

**Question 7.** Find distance between A(10 cos θ, 0) and B(0, 10 sin θ).

**Question 8.** If A(5, 2), B(2, -2) and C(-2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t. (CBSE 2015)

**Question 9.** Prove that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle. (CBSE 2013)

**Question 10.** Find the value of y for which the distance between the points A (3,-1) and B (11, y) is 10 units. (CBSE 2011)

**Question 11.** If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), then find the value of p. (CBSE 2012)

**Question 12.** If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b), prove that bx = ay. (CBSE 2016)

**Question 13.** If the point P(2, 2) is equidistant from the points A(-2, k) and B(-2k, -3), find k. Also find the length of AP. (CBSE 2014D)

**Question 14.** Prove that the points A(0, -1), B(-2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD. (CBSE 2013D)

**Question 15.** Prove that the points A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2) are the vertices of a rhombus ABCD. Is ABCD a square? (CBSE 2013OD)

**Question 16.** If P(2, 4) is equidistant from Q(7, 0) and R(x, 9), find the values of x. Also find the distance P (CBSE 2011D)

**Question 17.** Two friends Seema and Aditya work in the same office at Delhi. In the Christmas vacations, both decided to go to their hometowns represented by Town A and Town B respectively in the figure given below. Town A and Town B are connected by trains from the same station C (in the given figure) in Delhi. Based on the given situation, answer the following questions.

(i) Who will travel more distance, Seema or Aditya, to reach to their hometown?

(ii) Seema and Aditya planned to meet at a location D situated at a point D represented by the mid-point of the line joining the points represented by Town A and Town B. Find the coordinates of the point represented by the point D.

[CBSE SQP 2019 (Standard)]

**Question 18. **Find the point on y-axis which is equidistant from the points (5, -2) and (-3, 2).

**Question 19.** If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay. [CBSE Outside Delhi 2016]

**Question 20.** Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order.