Question

In what ratio the line segment joining the points (-1, 3) and (4, -7) divided by the point (2, -3)?

• A. 3:5
• B. 5:3
• C. 3:2
• D. 2:7

Answer 1

The correct option is C

3:2

From section formula, if a point $(x,y)$ divides the line segment joining the points ($x_1,y_1$) and ($x_2,y_2$) internally in the ratio m:n, then $x=\frac{m{x}_2+n{x}_1}{m+n}$ and $y=\frac{m{y}_2+n{y}_1}{m+n}$.

So, $2=\frac{4m+n(-1)}{m+n}$

$⟹4m-n=2m+2n$

i.e., $2m=3n$

Thus, $\frac{m}{n}$ = $\frac{3}{2}$ or $m:n=3:2$