Question

$X=0$ divides line segment joining points $P(2,4)$ and $Q(8,-8)$ in the ratio $2:3$

• A. True
• B. False

Answer 1

The correct option is B False

Here we apply the section formula, i. e. if a point $A(x,y)$ divides the line segment $PQ$ joining the points $P(x_1,y_1)\&Q(x_2,y_2)$ in the ratio $m:n$ then we have

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

Since $P=(2,4)$ and $Q=(8,-8)$ and $X=0$ means the Y-axis

$\therefore$ $A=(0,y)$
Let required ratio be $k:1$.
So, $0=\frac{k\left(8\right)+1\left(2\right)}{k+1}$

$\therefore 8k+2=0,k=-\frac{2}{8}$

$K=-\frac{1}{4}$

Not possible $x=0$ is Y-axis and it does not divide the line segment joining PQ.