Question

Find the ratio in which the point $(2,y)$ divides the line segment joining the points $A(-2,2)$ and $B(3,7)$. Also, find the value of $y$.

Answer 1

Let the points divide in $b:1$

Here $m=b$ and $n=1$

$A(-2,2)\equiv (x_1,y_1)$ and $B(3,7)\equiv (x_2,y_2)$
B(3,7)

we know that if point $(x,y)$ divides line in m:n

$x=\frac{m{x}_2+n{x}_1}{m+n}$ and $y=\frac{m{y}_2+n{y}_1}{m+n}$

$2=\frac{3b-2}{b+1}$

$2b+2=3b-2$

$b=4$

$y=\frac{4\left(7\right)+2}{4+1}$

$y=\frac{30}{5}$

$\therefore b=4andy=6$

$Ratio=b:1=4:1$