Question

The image of a point P on reflection in the y axis is Q. The mid point of PQ is invariant on reflection in the x axis. Locate the origin.

• A. Point P
• B. Point Q
• C. Midpoint of PQ
• D. Cannot be determined.

Answer 1

The correct option is C

Midpoint of PQ

Let point P be $P(x,y)$

$\therefore M_y(x,y)=Q(-x,y)$

Midpoint of $PQ=(\frac{x-x}{2},\frac{y+y}{2})$

$=(0,y)\Rightarrow$ this point lies on y axis .......(1)

Given - (0, y) is invariant on reflection in x axis

$\Rightarrow$ the point lies on x axis and its y coordinate is 0.......... (2)

From (1) and (2) we can conclude

that the midpoint of PQ is the origin (0,0) as both x and y coordinates are 0.