Question

In what ratio, does $P(4,6)$ divide the join of $A(-2,3)$ and $B(6,7)$

• A. $1:2$
• B. $3:1$
• C. $4:1$
• D. $2:1$

Answer 1

Answer: (B)

$3:1$

We know that, the co-ordinates of the points which divide internally the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is

$P(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

$A(-2,3)$ and $B(6,7)$ are the end-points and point $P(4,6)$ divide the line.

Let point $P(4,6)$ divide the line internally in the ratio $m:n.$

$x$-coordinate of $P$$:4=\frac{6m+(-2n)}{m+n}$

$4\times (m+n)=6m-2n$

$4m+4n=6m-2n$

$2m=6n$

$\frac{m}{n}=\frac{3}{1}$

So, point $P(4,6)$ divide the line in the ratio $3:1.$