 # How to Reflect a Figure over a Line with a Compass

To reflect a figure about a line, you must move all the points on one side of the line to the other side. This should work in the same way as your reflected image does when you look in a mirror.

You can accomplish this in a very tiresome way—by moving every single point. Or, you can be a little smarter, and move strategic points, most often corners, so you can then draw the lines between them. Below are instructions for how to proceed.

Rule

1.
Construct a normal from the point $A$ to the mirror line $l$. Extend the normal so that it is further past the mirror line than $A$ is. Call the intersection of the normal and the mirror line ${X}_{1}$.
2.
Put the compass tip on ${X}_{1}$. Measure the distance from there to $A$ with the compass. Set the same distance along the normal, but on the opposite side of the mirror line. Call this intersection ${A}^{\prime }$.
3.
Repeat Steps 1 and 2 until all key points have their reflection on the other side of the line. Call them ${B}^{\prime }$, ${C}^{\prime }$, etc.
4.
Draw the lines between ${A}^{\prime }$, ${B}^{\prime }$, ${C}^{\prime }$, etc. to complete the reflection.

The figure shows a reflection of the line $AB$ on the line $l$: 