Question Video: Determining the Pair of Triangles That Represents a Reflection in the 𝑥-Axis Mathematics • First Year of Preparatory School

Video Transcript

Which pair of triangles represents a reflection in the 𝑥-axis?

To answer this question, we need to imagine placing a mirror along the 𝑥-axis. When we do this, all objects will be reflected onto the opposite side of the mirror. Objects that were originally above the mirror line will be reflected below it. And objects that were originally below the mirror line will be reflected above it. The image of each object will be the same size as the original. And each vertex will be the same distance away from the mirror, just in the opposite direction. By visualizing the effect reflection in the 𝑥-axis will have, we can see that triangles 𝐴 and 𝐵 represent a reflection in the 𝑥-axis.

We can also look more closely at each vertex. Taking triangle 𝐴 to be the object, we can see that the vertex negative two, two is originally two units above the 𝑥-axis. The image of this vertex is at negative two, negative two. The vertex is in the same horizontal position but is now two units below the 𝑥-axis. So it’s the same vertical distance from the mirror, but in the opposite direction. The same is true for each of the other two vertices. The pair of triangles that represents a reflection in the 𝑥-axis is 𝐴 and 𝐵.