### Video Transcript

Which pair of triangles represents
a reflection in the ๐ฅ-axis?

The ๐ฅ-axis is this horizontal
line. We could call that the line with
equation ๐ฆ equal zero. Now, weโre 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 theyโll be located the same distance from the ๐ฅ-axis but on opposite
sides. So, letโs look at some of these
pairs.

Weโll begin by looking at shape ๐ด
and ๐ต. For shape ๐ด and ๐ต, 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 ๐ฅ-axis on opposite sides. And the shape is flipped but
otherwise unchanged. That is indeed a reflection in the
๐ฅ-axis. So, thatโs a good indication of us
that the pair of triangles that represent the relevant reflection are ๐ด and ๐ต. But letโs check and see whatโs
happened between the other pairs.

Letโs look at shape ๐ด and ๐ถ. Once again, comparing the relevant
vertices of our shapes, we see that they are the same distance from the ๐ฆ-axis on
opposite sides. And the shape is flipped over the
๐ฆ-axis but otherwise unchanged. In this case then, shapes ๐ด and ๐ถ
represent a reflection in the ๐ฆ-axis.

Now, what about shapes ๐ต and
๐ถ? Well, there are two ways to
describe this. We add in a diagonal line with the
equation ๐ฆ equals negative ๐ฅ. Now, we compare the vertices of ๐ต
and ๐ถ. This time, our vertices are the
same distance from the line ๐ฆ equals negative ๐ฅ but on opposite sides. Otherwise, shapes ๐ต and ๐ถ, apart
from being flipped โ remember, thatโs a reflection โ remain the same shape and
size. So, we could say that shapes ๐ต and
๐ถ represent a reflection in the line ๐ฆ equals negative ๐ฅ.

If we look carefully though, we can
even say the shape has been rotated 180 degrees about the origin. Thatโs the point zero, zero. In this case though, the pair of
triangles we were looking for were ๐ด and ๐ต.