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Find the coordinates of the points which divide the line segment joining the points (5, 7) and (8, 10) in 3 equal parts.

Answers (1)

Given :

$A=(x_1,y_1)=(5,7)$

$B=(x_2,y_2)=(8,10)$

Let P and Q are two points such that

$AP=PQ=QB$

$\Rightarrow$ P divides AB in 1 : 2 $\Rightarrow m:n=1:2$

$\Rightarrow$ Q divides AB in 2 : 1 $\Rightarrow m:n=2:1$

$\text{Coordinates of P}= \left ( \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n} \right )$

Here, $m=1,n=2$

$P= \left ( \frac{1\times 8+2\times 5}{1+2},\frac{1\times 10+2\times 7}{1+2} \right )$

$P= \left ( \frac{ 8+10}{3},\frac{10+14}{3} \right )$

$P= \left ( \frac{18}{3},\frac{24}{3} \right )$

$P= \left ( 6,8 \right )$

$\text{Coordinates of Q}= \left ( \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n} \right )$

Here $m=2,n=1$

$Q= \left ( \frac{2\times 8+1\times 5}{2+1},\frac{2\times 10+1\times 7}{2+1} \right )$

$Q= \left ( \frac{16+5}{3},\frac{20+7}{3} \right )$

$Q= \left ( \frac{21}{3},\frac{27}{3} \right )$

$Q= \left ( 7,9 \right )$

Coordinates of P = (6,8) and Q = (7,9)

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