Question

A straight line passes through the points $P(-1,4)$ and $Q(5,-2).$ It intersects the co-ordinate axes at points A and B. M is the mid-point of the segment AB. Find the co-ordinates of M.

Answer 1

Given points, $P(-1,4)$ and $Q(5,-2)$

Slope of $PQ=\frac{(-2-4)}{(5+1)}=-\frac{6}{6}=-1$

Equation of the line PQ is given by,

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

$y-4=-1(x+1)$

$y-4=-x-1$

$x+y=3$

For point A (on x-axis), $y=0.$

So, putting $y=0$ in the equation of PQ, we have

$x=3$

Hence, the co-ordinates of point A are $(3,0).$

For point B (on y-axis), $x=0.$

So, putting $x=0$ in the equation of PQ, we have

$y=3$

Hence, the co-ordinates of point B are $(0,3).$

M is the mid-point of AB.

Thus, the co-ordinates of point M are

$(\frac{3+0}{2},\frac{0+3}{2})=(\frac{3}{2},\frac{3}{2})$