Which pair of triangles represents
a reflection in the 𝑥-axis?
The 𝑥-axis is this horizontal
line. We could call that the line with
equation 𝑦 equal zero. Now, we’re looking for the pair of
triangles which represent a reflection in this line. Now, when we reflect a shape, we
flip it. The two triangles will have the
same size, and they’ll be located the same distance from the 𝑥-axis but on opposite
sides. So, let’s look at some of these
We’ll begin by looking at shape 𝐴
and 𝐵. For shape 𝐴 and 𝐵, this first
vertex is two units away from our mirror line. For both shapes, this second vertex
is five units away from the mirror line on opposite sides. And our third vertices are both
three units away from the mirror line on opposite sides. We see that each of the points are
the same distance from the 𝑥-axis on opposite sides. And the shape is flipped but
otherwise unchanged. That is indeed a reflection in the
𝑥-axis. So, that’s a good indication of us
that the pair of triangles that represent the relevant reflection are 𝐴 and 𝐵. But let’s check and see what’s
happened between the other pairs.
Let’s look at shape 𝐴 and 𝐶. Once again, comparing the relevant
vertices of our shapes, we see that they are the same distance from the 𝑦-axis on
opposite sides. And the shape is flipped over the
𝑦-axis but otherwise unchanged. In this case then, shapes 𝐴 and 𝐶
represent a reflection in the 𝑦-axis.
Now, what about shapes 𝐵 and
𝐶? Well, there are two ways to
describe this. We add in a diagonal line with the
equation 𝑦 equals negative 𝑥. Now, we compare the vertices of 𝐵
and 𝐶. This time, our vertices are the
same distance from the line 𝑦 equals negative 𝑥 but on opposite sides. Otherwise, shapes 𝐵 and 𝐶, apart
from being flipped — remember, that’s a reflection — remain the same shape and
size. So, we could say that shapes 𝐵 and
𝐶 represent a reflection in the line 𝑦 equals negative 𝑥.
If we look carefully though, we can
even say the shape has been rotated 180 degrees about the origin. That’s the point zero, zero. In this case though, the pair of
triangles we were looking for were 𝐴 and 𝐵.