## AP State Syllabus SSC 10th Class Maths Solutions 7th Lesson Coordinate Geometry Optional Exercise

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 7 Coordinate Geometry Optional Exercise Textbook Questions and Answers.

### 10th Class Maths 7th Lesson Coordinate Geometry Optional Exercise Textbook Questions and Answers

Question 1.

Centre of the circle Q is on the Y-axis. And the circle passes through the points (0, 7) and (0, -1). Circle intersects the positive X-axis at (p, 0). What is the value of ‘p’ ?

Answer:

Given points A, B are on y – axis.

(∵ their x – coordinate is zero) then they will be the end points (0, 7) and (0, -1).

Centre (Q) = \(\left(\frac{0+0}{2}, \frac{7-1}{2}\right)\) = (0, 3)

then radius = AQ = BQ

= \(\sqrt{(0-0)^{2}+(3-(-1))^{2}}\)

= \(\sqrt{0^{2}+4^{2}}\) = √16 = 4

now P(p, 0) is also another point on circle then \(\overline{\mathrm{QP}}\) is also radius

∴ \(\overline{\mathrm{QP}}\) = \(\sqrt{(0-p)^{2}+(3-0)^{2}}\) = 4

⇒ \(\sqrt{p^{2}+3^{2}}\) = 4

⇒ p^{2} = 4^{2} – 3^{2} = 16 – 9 = 7

∴ P = ± √7 .

Question 2.

A triangle ABC is formed by the points A(2, 3), B(-2, -3), C(4, -3). What is the point of intersection of side BC and angular bisector of angle A?

Answer:

Given: △ABC, where A (2, 3), B (- 2, – 3), C (4, – 3).

Let AD be the bisector to ∠A meeting BC at D.

Then BD : DC = AB : AC

[∵ The bisector of vertical angle of triangle divides the base in the ratio of other two sides.]

Now D is a point which divides \(\overline{\mathrm{BC}}\) in the ratio √l3 : √10 internally section formula (x, y) =

(By rationalising the denominator of the x-coordinate).

Question 3.

The side BC of an equilateral △ABC is parallel to X – axis. Find the slopes of line along sides BC, CA and AB.

Answer:

Given: △ABC; BC // X – axis.

Slope of BC = tan θ

where θ is the angle made of BC with + ve X – axis.

= tan ‘0’ = ‘0’

Slope of AB = tan 60° = √3

[∵ Each angle of an equilateral triangle is 60°]

Slope of AC = tan 60° = √3

Question 4.

A right triangle has sides ‘a’ and ‘b’ where a > b. If the right angle is bisected then find the distance between ortho centres of the smaller triangles using coordinate geometry.

Answer:

Given : △ABC; ∠B = 90°

Question 5.

Find the centroid of the triangle formed by the line 2x + 3y – 6 = 0 with the coordinate axes.

Answer:

Given : △AOB formed by the line 2x + 3y – 6 = 0 with axes.

Let A lie on X – axis and B on Y – axis.

∴ Y – coordinate of A = 0

X – coordinate of B = 0

∴ A (3, 0), B (0, 2)