Video Transcript
Find the coordinates of the
images of the points 𝐴, 𝐵, 𝐶, and 𝐷 after reflection in the 𝑦-axis.
To reflect these points in the
𝑦-axis, we need to imagine placing a mirror along the 𝑦-axis. The mirror is vertical, so the
effect of reflecting in this line will be horizontal. Any point in the coordinate
plane will be reflected onto the opposite side of the mirror and will appear the
same distance behind the mirror as it originally was in front of the mirror.
Let’s start with point 𝐴,
which has coordinates eight, six. This point is eight units to
the right of the mirror. So its image will appear eight
units to the left of the mirror at the same vertical height. The image of point 𝐴 will
therefore be negative eight, six.
Point 𝐵 has coordinates eight,
one and is directly below point 𝐴. The image of point 𝐵 will
therefore be directly below the image of point 𝐴, so with an 𝑥-coordinate of
negative eight, and will have the same 𝑦-coordinate as the original point
𝐵. The image of point 𝐵 is the
point negative eight, one.
The coordinates of points 𝐶
and 𝐷 are two, one and two, six, respectively. Each of these points is two
units to the right of the mirror. So their image will be two
units to the left of the mirror. The images of points 𝐶 and 𝐷
are therefore at negative two, one and negative two, six, respectively. If we were to join the images
of the four vertices together, we can see that the shape created is congruent to
the original rectangle 𝐴𝐵𝐶𝐷.
It isn’t immediately obvious
because this shape is symmetrical, but its orientation has also changed. The coordinates of the images
of points 𝐴, 𝐵, 𝐶, and 𝐷 are negative eight, six; negative eight, one;
negative two, one; and negative two, six.
