Question

In what ratio does the point P(-2, 3) divide the line segment joining the points A(-3, 5) and B(4, -9) internally?

• A. 1 : 2
• B. 1 : 6
• C. 1 : 4
• D. 1: 5

Answer 1

Answer: (B)

1 : 6

Let the ratio be $k:1$

Substituting $(x_1,y_1)=(-3,5)$ and $(x_2,y_2)=(4,-9)$ in the
section formula, we get $(\frac{k\left(4\right)+1(-3)}{k+1},\frac{k(-9)+1\left(5\right)}{k+1})=(-2,3)$

$(\frac{4k-3}{k+1},\frac{-9k+5}{k+1})=(-2,3)$

Comparing the x - coordinate,
$=>\frac{4k-3}{k+1}=-2$
$=>4k-3=-2k-2$

$6k=1$

$k=\frac{1}{6}$

Hence, the ratio is $1:6$