AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 7 Coordinate Geometry Ex 7.2 Textbook Questions and Answers.

## AP State Syllabus SSC 10th Class Maths Solutions 7th Lesson Coordinate Geometry Exercise 7.2

### 10th Class Maths 7th Lesson Coordinate Geometry Ex 7.2 Textbook Questions and Answers

Question 1.

Find the coordinates of the point which divides the line segment joining the points (-1, 7) and (4, -3) in the ratio 2 :3.

Answer:

Given points P (-1, 7) and Q (4, – 3). Let ‘R’ be the required point which divides \(\overline{\mathrm{PQ}}\) in the ratio 2:3. Then

Question 2.

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

Answer:

Given points A (4, – 1) and B (- 2, – 3) Let P and Q be the points of trisection

of \(\overline{\mathrm{AB}}\), then AP = PQ = QB.

∴ P divides \(\overline{\mathrm{AB}}\) internally in the ratio 1 : 2.

Also, Q divides \(\overline{\mathrm{AB}}\) in the ratio 2 : 1 internally.

Question 3.

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

Answer:

Let the point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in a ratio of m : n

⇒ 6m – 3n = -(m + n) = -m – n

⇒ 6m + m = – n + 3n

⇒ 7m = 2n

⇒ \(\frac{m}{n}=\frac{2}{7}\)

⇒ m : n = 2 : 7

∴ The point (-1, 6) divides the given line segment in a ratio of 2 : 7.

Question 4.

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

Answer:

Given: ▱ ABCD is a parallelogram where A (1, 2), B (4, y), C (x, 6) and D (3, 5).

In a parallelogram, diagonals bisect each other.

i.e., the midpoints of the diagonals coincide with each other.

i.e.,midpoint of AC = midpoint of BD

⇒ 1 + x = 7 and 8 = y + 5

⇒ x = 7 – 1 and y = 8 – 5

∴ x = 6 and y = 3.

Question 5.

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).

Answer:

Given:

A circle with centre ‘C’ (2, -3). \(\overline{\mathrm{AB}}\) is a diameter where

B = (1, 4); A = (x, y).

C is the midpoint of AB.

[∵ Centre of a circle is the midpoint of the diameter]

4 = x + 1 and – 6 = y + 4

⇒ x = 4 – 1 = 3 and y = -6 – 4 = -10

A (x, y) = (3, -10)

Question 6.

If A and B are (-2, -2) and (2, -4) respectively. Find the coordinates of P such that AP = \(\frac{3}{7}\) AB and P lies on the segment AB.

Answer:

Given: A (- 2, – 2) and B (2, – 4)

P lies on AB such that AP = latex]\frac{3}{7}[/latex] AB

i.e., P divides \(\overline{\mathrm{AB}}\) in the ratio 3 : 4 By section formula,

Question 7.

Find the coordinates of points which divide the line segment joining A (-4, 0) and B (0, 6) into four equal parts.

Answer:

Given, A (- 4, 0) and B (0, 6).

Let P, Q and R be the points which divide AB into four equal parts.

P divides \(\overline{\mathrm{AB}}\) in the ratio 1 : 3, Q → 1 : 1 and R → 3 : 1 Use section formula to find P, Q and R.

Then, Q is the midpoint of \(\overline{\mathrm{AB}}\)

P is the midpoint of \(\overline{\mathrm{AQ}}\)

R is the midpoint of \(\overline{\mathrm{QB}}\)

Question 8.

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

Answer:

Given, A (- 2, 2) and B (2, 8).

Let P, Q and R be the points which divide AB into four equal parts.

Then, Q is the midpoint of \(\overline{\mathrm{AB}}\)

P is the midpoint of \(\overline{\mathrm{AQ}}\)

R is the midpoint of \(\overline{\mathrm{QB}}\)

Question 9.

Find the coordinates of the point which divide the line segment joining the points (a + b, a-b) and (a-b, a + b) in the ratio 3 : 2 internally.

Answer:

Given : A (a + b, a – b) and B (a – b, a + b).

Let P (x, y) divides \(\overline{\mathrm{AB}}\) in the ratio 3 : 2 internally.

Section formula

Question 10.

Find the coordinates of centroid of the triangle with following vertices:

i) (-1, 3), (6, -3) and (-3, 6)

Answer:

Given: △ABC in which- A (- 1, 3), B (6, -3) and C (-3, 6)

ii) (6, 2), (0, 0) and (4, -7)

Answer:

Given: The three vertices of a triangle are A (6, 2), B (0, 0) and C (4, – 7).

Centroid (x, y)

iii) (1,-1), (0, 6) and (-3, 0)

Answer:

Given: (1, -1), (0, 6) and (-3, 0) are the vertices of a triangle.

Centroid (x, y)