Question

In what ratio is the line segment joining (-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 (x,y) divides the line segments joining ($x_1,y_1$) and ($x_2,y_2$) internally in the ratio of 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 = $\frac{4m+n(-1)}{m+n}$,

$\Rightarrow$ 2m +2n = 4m - n

$\Rightarrow$ 3n = 2m

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