Question

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.

Answer 1

According to the question,

Given that,

PR = `3/5`PQ

⇒ `("PQ")/("PR") = 5/3`

⇒ `("PR" + "RQ")/("PR") = 5/3`

⇒ `1 + ("RQ")/("PR") = 5/3`

⇒ `("PQ")/("PR") = 5/3 - 1 = 2/3`

∴ RQ : PR = 2 : 3

or PR : RQ = 3 : 2

Suppose, R(x, y) be the point which divides the line segment joining the points P(–1, 3) and Q(2, 5) in the ratio 3 : 2

∴ (x, y) = `{(3(2) + 2(-1))/(3 + 2), (3(5) + 2(3))/(3 + 2)}`   ...`[∵ "By internal section formula", {(m_2x_1 + m_1x_2)/(m_1 + m_2), (m_2y_1 + m_1y_2)/(m_1 + m_2)}]`

= `((6 - 2)/5, (15 + 6)/5)`

= `(4/5, 21/5)`

Hence, the required coordinates of the point R is `(4/5, 21/5)`.