In what ratio the line segment joining the points (-1, 3) and (4, -7) di

Question

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

Options:

A . 3:5

B . 5:3

C . 3:2

D . 2:7

Answer: Option C
:
C

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

$⟹ 4 m - n = 2 m + 2 n$

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

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

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