Question

If the perpendicular distance of a point $P$ from the $X$axis is $5$ units and the foot of perpendicular is on the negative direction of $X$ axis, then find the $Y$ coordinate of $P$.

Answer 1

Given PQ=5

Case (i) [REF.Image]

Let $P=(-x,y)$ and $Q=(-x,0)$

$PQ=5=\sqrt{(-x+x{)}^2+(0-y{)}^2}$

$5=\sqrt{0+y^2}$

$y=5$

Case (ii) [REF.Image]

Let $P(-x,-y)+Q(-x,0)$

$PQ=5=\sqrt{(-x+x{)}^2+(-y-0{)}^2}$

$y=5$

y-co-ordinate of $P=(5,-5)$