Gujarat Board Solutions Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2

Gujarat Board Solutions Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2

Gujarat Board Textbook Solutions Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2

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.
Solution:
Let the given points be A(-1, 7) and B(4, -3).
Here, we have
x₁ = -1, y₁ = 7
x₂ = 4, y₂ = -3
and m₁ = 2, m₂ = 3
Let the required point be P(x, y).

Question 2.
Find the coordinates of the points of tri-section of the line segment joining (4, -1) and (-2, -3).
Solution:
Let P and Q be the points of the tri-section of AB.
Then,
AP = PQ = QB = 1
Case I: Here P divides AB in the ratio 1 : 2.
So, we have
x₁ = 4, y₁ = -1
x₂ = -2, y₁ = -3
and m₁ = 1, m₂ = 2
∴ The coordinates of P are given by

Question 3.
To conduct Sports Day activities in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in Figure. Niharika runs 1/4th the distance AD on the 2 line and posts a green flag. Preet runs 1/5th distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Question 4.
Find the ratio in which the segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Solution:
Let P(-1, 6) divides the line segment joining the points A(-3, 10) and B(6, -8) in the ratio k: 1.
Then the coordinates of P are given by –

Question 5.
Find the ratio in which the line segment joining A(1, -5) and B(-4, 5) is divided by the x-axis. Also find the coordinates of the point of divisions.
Solution:
Let the given points be A(1, -5) and B(-4, 5).
Let the x-axis cuts AB at the point P in the ratio k :1.
Then, the coordinates of P are given as

Here, we have
x₁ = 1, y₁ = -5
x₂ = -4 y₂ = 5
and m₁ = k, m₁ = 1
So, coordinates of P are

Question 6.
If(1, 2), (4,y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Solution:
Let A(1, 2), B(4, y), C(x, 6) and D(3, 5) are the vertices of a parallelogram.

Question 7.
Find the coordinates of point A, where AB is the diameter of a circle whose center is (2, -3) and B is (1, 4).
Solution:
Let the given point be A(x, y). Since C is the mid-point of AB.

Question 8.
If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = AB and P lies on the line segment AB.
Solution:

Question 9.
Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts.
Solution:
Let P, Q and R be the three points that divide the line segment joi fling the points A(-2, 2) and (2, 8) in four equal parts.
Case I: For point P, we have

Question 10.
Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.
Solution:
Let the given points are A(3, 0), B(4, 5), C(-1, 4)
and D(-2, -1).
We have,

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