Question
In what ratio does the point $P(-4, y)$ divide the line segment joining the points $A (-6,10)$ and $B (3,-8)$ ? Hence find the value of $y$.
✓
Answer
Let the point $P$ divide the line segment $A B$ into $m : n$ Using section formula
$\therefore-4=\frac{3 \times m+(-6) \times n}{m+n}$
$\Rightarrow-4(m+n)=3 m-6 n$
$\Rightarrow-4 m-4 n=3 m-6 n$
$\Rightarrow-4 m-3 m=-6 n+4 n$
$\Rightarrow-7 m=-2 n$
$\Rightarrow \frac{m}{n}=\frac{2}{7}$
$m: n=2: 7$
Using section formula,
$y=\frac{2 \times-8+7 \times 10}{2+7}$
$\therefore-4=\frac{3 \times m+(-6) \times n}{m+n}$
$\Rightarrow-4(m+n)=3 m-6 n$
$\Rightarrow-4 m-4 n=3 m-6 n$
$\Rightarrow-4 m-3 m=-6 n+4 n$
$\Rightarrow-7 m=-2 n$
$\Rightarrow \frac{m}{n}=\frac{2}{7}$
$m: n=2: 7$
Using section formula,
$y=\frac{2 \times-8+7 \times 10}{2+7}$
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