Question

Show that the point $P(-4,2)$ lies on the line segment joining the points $A(-4,6)$ and $B(-4,-6)$

Answer 1

A line segment joining the points $A$ and $B$ is :

$y-y_1=m(x-x_1)$

$\Rightarrow y-6=\frac{-6-6}{-4+4}(x+4)$

$\Rightarrow x+4=0$

If point P lies on the given line then it must satisfy the equation of the line,

Therefore,

$x+4=0$

$\Rightarrow -4+4=0$

$\Rightarrow 0=0$

Hence, point $P$ lies on the line $AB$