How to Reflect a Shape over a Line Using a Compass

Last Updated: February 24, 2023

If you're taking a geometry course in middle or high school, you will need to learn how to reflect points and shapes across lines. This is an extension to beginner reflections (basically drawing a shape on a piece of paper and folding it in half to understand what reflections are) that you may have done in elementary school. The reflections you will learn now are more precise, as you actually use points on the coordinate plane to reflect over a line. This article will teach you how to reflect a shape over a line using a protractor.

Steps

1
Draw one arc intersecting your line of reflection. Using your compass, put the compass needle on your point, set it to intersect your line, and draw an arc. Swing the compass to get an arc. You can also draw two separate, smaller arcs; one on the left side of the line and one on the right side of the line.
2
Draw two more arcs. First, place the compass needle on the very left of your arc. Make sure you don't change the angle of the compass. Then, swivel your needle to make the pencil part of the compass draw a small arc. Do the same steps for the other arc. First, place the compass needle on the very right of your arc this time. Then, do not change the compass setting and swivel your compass needle to make the pencil draw a small arc. ^{[1]
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- The two arcs should be intersecting. If your two arcs are not intersecting, you may have accidentally changed the compass setting.
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3
Mark your reflected point. The intersection of your two small arcs is your reflected point. Mark this point as (name of point)'. The apostrophe is used to mark similar points or shapes. It is used to mark points and shapes that have been reflected, translated, rotated, or dilated.
- For example, if your original point was A, mark your reflected point A'.
4
Do this for the other points of your shape. The process of reflecting multiple points over a line will give you a reflected shape. First, start from one of the points of your shape. Secondly, extend the compass from your point to your line of reflection and draw an arc intersecting it. Next, draw a smaller arc without changing the compass setting starting from the left of your first arc. Then, draw another small arc from the right of your first arc. Lastly, mark the small arcs' intersection as (name of point)'.
- This is read as "(name of point) prime".