Question

Find the points of trisection of the line segment joining the points $A(2,-2)$ and $B(-7,4)$.

• A. $(-1,0)$ and $(-4,2)$
• B. $(1,0)$ and $(-4,2)$
• C. $(-1,0)$ and $(4,2)$
• D. None of these

Answer 1

Answer: (A)

$(-1,0)$ and $(-4,2)$

Given:- $A(2,-2)$ and $B(-7,4)$

For point of trisection, $AB$ is divided into $3$ equal parts.

Let the two trisection points are $P(x,y)$ and $Q(c,d)$.

Hence $P$ divides $AB$ in ratio $1:2$ and $Q$ divides $AB$ in ratio $2:1$.

By section formula:

$x=\frac{m{x}_2+n{x}_1}{m+n}$ and $y=\frac{m{y}_2+n{y}_1}{m+n}$

$x=\frac{4-7}{3}=-1$ and $y=\frac{4-4}{3}=0$

So,$P(x,y)=(-1,0)$.

Again by section formula:

$c=\frac{-14+2}{3}=-4$ and $d=\frac{8-2}{3}=2$

So, $Q(c,d)=(-4,2)$.