4 Essential Steps for Reflection in Math

What are the Rules for Reflections? Here’s everything you need to know.

Read the Concise Reflection in Geometry Definition

So what is a reflection in math anyway? Well, a Reflection in Math happens when a figure makes an identical mirrored representation of itself across either the x-axis or y-axis. You can Reflect in Math by changing the sign on the x-values or y-values of the figure. The x-values will change signs when reflecting over the y-axis. The y-values change signs when reflecting over the x-axis. Make sure you label your vertices when drawing your new figure on the coordinate grid.

 

Reflection in Math Practice Problems Quiz

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Video Transcript:

Reflection in math refers to a way to transform a shape on the coordinate grid. When you think of reflection math, you can think of it as creating a mirror image of a figure. Reflection in math occurs typically over either the y-axis or the x-axis. This is the broad reflection geometry definition for reflections in math.

When reflecting over the y-axis you have to imagine that the y-axis is a mirror and whatever is on this side of the mirror is going to be reflected on this side of the mirror. If we were to reflect this triangle across the y axis reflection it would create a mirror image on this side of the y axis of that triangle. The mirror image across the y axis of this triangle looks like this. You can also reflect over x axis. When you reflect over x axis it will look exactly the same as the original figure, except it will be in this quadrant and reflected as if the x axis was a mirror that you held up to this figure. You can see that the green triangle is a mirror reflection of the red triangle except it is inverted because it’s been reflected across the x axis.

There are a couple of shortcuts for reflecting coordinates across the X or the y axis. When reflecting across the x axis your coordinates, which would be X and Y, will change. The x coordinate will stay the same and the sign on the y coordinate will change. If it’s positive it’ll become negative, if it’s negative it’ll become positive. The same type of rule applies for the y axis except when reflecting across the y axis, in order to change your coordinates, this time the x coordinate sign will change. If it’s negative, it becomes positive and vice-versa and the Y will stay the same.

An easy way to remember which coordinate stays the same is that which ever axis you’re reflecting across that coordinate will stay the same. When doing an x axis reflection, the x coordinate stays the same and if you reflect across the Y axis the y coordinate stays the same.

Here we are at the first practice problem on our reflection in math worksheet. Number 1 says to reflect figure ABCD over the y axis which will be a reflection over y axis. In order to do this we have to take our figure ABCD and we have to draw it with a reflection across the y-axis which is the vertical axis in the middle of the grid. This shape will be reflected across the Y axis on to this side of the y axis because we’re reflecting over the y axis. We already know how our coordinates are going to change. We know that our X and our Y coordinates are going to change the sign of our x coordinate and keep the sign on the y coordinate the same.

When looking at our coordinates of our original figure we know that what we’re going to do is we’re going to keep the sign of the Y the same. If you look at a the coordinate is negative 8 2. We know that the Y value is going to stay 2 because it will not change and that the sign on the x value will change. This is negative 8 so now it will become positive 8. For coordinate B our coordinate is negative 4 positive 2. We know that the 2 and the y value will stay the same but the negative 4 will become positive because we have to change the sign on the x value. Coordinate c is negative 3 negative 2. We know that X has to change so this is negative it has to become positive and we know that the negative 2 for the Y value will remain negative 2. And then finally D gives us negative 8 negative 2. The negative 8 will become positive 8 and the negative 2 will remain the same.

The last step is to graph the new figure after it’s been reflected across the Y axis. I’ve rewritten our new coordinates here right next to the grid to make it easier to graph. A prime is 8 2 so we’re going to go ahead and graph that and then we’re going to label it a prime. B prime is 4 2 which is right here, C prime is 3 negative 2 and we’re going to label it, and then D prime is 8 negative two and we’ll label it here. The last step is to connect all of our coordinates so that we make our new figure. You can see that the new figure is a complete reflection of the original figure and it looks like you held up a mirror across the y-axis. This new figure is going to be the solution for this reflection in math problem.