# Thread: Find the length for PR

1. ## Find the length for PR

(page490)
From the attachment, P, Q, R are suppose to be different points.

In the figure above, ABCD is a rectangle with BC=4 and AB=6. Points P, Q, and R are different points on a line (not shown) that is parallel to line segment AD. Points P and Q are symmetric about line AB and points Q and R are symmetric about line CD. What is the length of line segment PR?

The correct answer is 8. Can you kindly show me the steps?

2. So line PQR is parall4el to the horizontal bottom side AD.

"Points P and Q are symmetric about line AB ...."
That means P and Q are equidistant from vertical side AB.

"....and points Q and R are symmetric about line CD."
Likewise, Q and R are equidistant from the vertical side CD.

Let point Q be anywhere inside the rectangle ABCD.
Say, Q is x away from AB.
Hence, Q is (4 -x) away from CD.

Then P is x away from AB, and R is (4 -x) away from CD.
So, for the total length of line PQR,
PR = x +x +(4 -x) +(4 -x) = 8 --------------answer.