Question

In the diagram, MN and KL are straight lines. Of the points marked P, Q, R and S which point lies on the perpendicular bisectors of both MN and KL?

Answer 1

Hint:
Firstly, draw the perpendicular bisectors on the lines MN and KL respectively.
Thus, observe after doing the above step that which of the points from the points P, Q, R and S is shared by both the perpendicular bisectors and choose the point carefully.

Complete step by step solution:
It is given that; MN and KL are straight lines denoted by red line segments.

We are asked to find which point of the points P, Q, R and S lies on the perpendicular bisectors of the lines MN and KL.
So, we have to draw perpendicular bisectors of the lines MN and KL.

The perpendicular bisector of the line MN is shown by the blue colored line and the perpendicular bisector of the line KL is shown by the green colored line in the above diagram.
On drawing the perpendicular bisectors of both the lines MN and KL, as shown in above figure, it can be seen that both perpendicular bisectors share a common point Q.

Thus, point Q lies on the perpendicular bisectors of both MN and KL.

Note:
Perpendicular bisector:
A line segment which is perpendicular to another line and also divides the line into two equal parts is called a perpendicular bisector of that line.
Properties of a perpendicular bisector of a line XY:
1) It divides the line XY into two equal halves.
2) It makes a right angle on the line.
3) Let A be any point on the perpendicular bisector. Then, A is always equidistant from the points X and Y.