Question

If the perpendicular distance of a point $Q$ from the $x$-axis is $3$ units, and the foot of its perpendicular to the $x$-axis lies on the negative direction of the $x$-axis, then the point $Q$ has:

• A. $x$-coordinate = $-3$
• B. $y$-coordinate = $3$ only
• C. $y$-coordinate = $-3$ only
• D. $y$-coordinate = $3$ or $-3$

Answer 1

The correct option is D $y$-coordinate = $3$ or $-3$

We know that the perpendicular distance of a point from the $x$-axis, along with the direction, gives the $y$-coordinate of that point.

Since the perpendicular distance of point $Q$ from the $x$-axis is $3$ units, its $y$-coordinate can be 3 or -3, depending on whether $Q$ is above or below the $x$-axis.

The additional data that the foot of its perpendicular to the $x$-axis lies on the negative direction of the $x$-axis only says that its $x$-coordinate is negative.

Thus, option (d) is correct.