Greetings and welcome to Mathsux! Today we are going to go over reflections, one of the many types of transformations that come up in geometry. And thankfully, it is one of the easiest transformation types to master, especially if you’re more of a visual learner/artistic type person. So let’s get to it!
What are Reflections?
Reflections on a coordinate plane are exactly what you think! When a point, a line segment, or a shape is reflected over a line it creates a mirror image. Think the wings of a butterfly, a page being folded in half, or anywhere else where there is perfect symmetry.
Step 1: First, let’s draw in line x=-2.
Step 2: Find the distance each point is from the line x=-2 and reflect it on the other side, measuring the same distance. First, let’s look at point C, notice it’s 1 unit away from the line x=-2, to reflect it we are going to count 1 unit to the left of the line x=-2 and label our new point, C|.
Step 3: Next we reflect point A in much the same way! Notice that point A is 2 units away on the left of line x=-2, we then measure 2 units to the right of our line and mark our new point, A|.
Step 4: Lastly, we reflect point B. This time, point B is 1 unit away on the right side of the line x=-2, we then measure 1 unit to the opposite side of our line and mark our new point, B|.
Step 5: Finally, we can now connect all of our new points, for our fully reflected triangle A|B|C|.
Still got questions? No problem! Check out the video above or comment below! Happy calculating! 🙂
Looking to review rotations about a point? Check out this post here!