Find the coordinates of the point R on the line segment joining the points P (–1, 3) and Q (2, 5) such that PR = 3/5 PQ
Solution:
Given, the point R lies on the line segment joining the points P(-1, 3) and Q(2, 5).
We have to find the coordinates of the point R such that PR = 3/5 PQ.
PR/PQ = 3/5
On rearranging,
PQ/PR = 5/3
We know that PQ = PR + QR
So, (PR + QR) / PR = 5/3
PR/PR + QR/PR = 5/3
1 + QR/PR = 5/3
QR/PR = 5/3 - 1
QR/PR = 5-3/3
QR/PR = 2/3
Again rearranging,
PR/QR = 3/2
PR : QR = 3 : 2
Therefore, the point R divides the line segment PQ in the ratio 3:2
The coordinates of the point P which divides the line segment joining the points A (x₁ , y₁) and B (x₂ , y₂) internally in the ratio m₁ : m₂ are
[(m₁x₂ + m₂x₁)/m₁ + m₂ , (m₁y₂ + m₂y₁)/m₁ + m₂]
Here, m₁ : m₂ = 3 : 2, (x₁ , y₁) = (-1, 3) and (x₂ , y₂) = (2, 5)
Let the coordinate of R = (x, y)
(x, y) = [(3(2) + 2(-1))/3 + 2, (3(5) + 2(3))/3 + 2]
(x, y) = [(6 - 2)/5, (15 + 6)/5]
(x, y) = [4/5, 21/5]
Therefore, the coordinates of point R are (4/5, 21/5).
✦ Try This: The line segment joining the points A(3, 2) and B(5,1) is divided at the point P in the ratio 1 : 2. Find the coordinates of the point P.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7
NCERT Exemplar Class 10 Maths Exercise 7.3 Problem 18
Find the coordinates of the point R on the line segment joining the points P (–1, 3) and Q (2, 5) such that PR = 3/5 PQ
Summary:
The coordinates of the point R on the line segment joining the points P (–1, 3) and Q (2, 5) such that PR = 3/5 PQ are (4/5, 21/5)
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