Question

If the perpendicular distance of a point $P$ from the $x-axis$ is $5$ units and the foot of the perpendicular lies on the negative direction of $x-axis$, then the point $P$ has

• A. $x-$ coordinate $=-5$
• B. $y-$coordinate $=$$5$ only
• C. $y-$ coordinate $=-5$ only
• D. $y-$coordinate $=-5$ or $5$

Answer 1

The correct option is D

$y-$coordinate $=-5$ or $5$

Explanation for correct option:

Find the coordinates based on given information

Given,

Perpendicular distance of a point $P$ from the $x$-axis is $5$ units and the foot of the perpendicular lies on the negative direction of $x-axis$.

The location of any point on a plane is expressed by a pair of values $(x,y)$ and these pairs are known as the coordinates.

We know that ,

In Quadrant $1:(+x,+y)$

In Quadrant $2:(-x,+y)$

In Quadrant $3:(-x,-y)$

In Quadrant $4:(+x,-y)$

Perpendicular distance from $x-axis$ $=$ Ordinate $=$ $5$

The negative direction of the $x-axis$ doesn’t decide the sign of the ordinate.

So, $y$ co-ordinate $=$ $5$ or $-5$

Hence, If the perpendicular distance of a point $P$ from the $x$-axis is $5$ units and the foot of the perpendicular lies on the negative direction of $x$-axis, then the point $P$ has $y$ co-ordinate $5$ or $-5$.