Question

Find the coordinates of the point R on the line segment joining the points P(-1,3) and Q(2,5) such that $PR=\frac{3}{5}PQ.$

• A. $(\frac{7}{5},\frac{21}{8})$
• B. $(\frac{4}{5},\frac{11}{5})$
• C. $(\frac{4}{7},\frac{21}{5})$
• D. $(\frac{4}{5},\frac{21}{5})$

Answer 1

The correct option is D

$(\frac{4}{5},\frac{21}{5})$

According to the question,

Given: $PR=\frac{3}{5}PQ$

$\Rightarrow \frac{PQ}{PR}=\frac{5}{3}$

$\Rightarrow \frac{PR+RQ}{PR}=\frac{5}{3}$

$\Rightarrow 1+\frac{RQ}{PR}=\frac{5}{3}$

$\Rightarrow \frac{RQ}{PR}=\frac{5}{3}-1=\frac{2}{3}$

$\therefore RQ:PR=2:3$ 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.

$\therefore (x,y)=\{\frac{3\left(2\right)+2(-1)}{3+2},\frac{3\left(5\right)+2\left(3\right)}{3+2}\}$

$\left[\begin{array}{c}\because \text{By internal section formula},\{\frac{m_2{x}_1+m_1{x}_2}{m_1+m_2},\frac{m_2{y}_1+m_1{y}_2}{m_1+m_2}\}\end{array}\right]$

$=(\frac{6-2}{5},\frac{15+6}{5})=(\frac{4}{5},\frac{21}{5})$

Hence, the required coordinates of the point R is $(\frac{4}{5},\frac{21}{5})$