Question Video: Finding the Coordinates of the Vertices of a Quadrilateral after Reflection Mathematics • 8th Grade

Video Transcript

Find the images of 𝐴𝐵𝐶𝐷 after reflection in the 𝑦-axis.

So here’s the line that we will be reflecting over. And it said to find the images. These points will be considered our preimages. So if we were to take our preimages and reflect over the 𝑦-axis, this line, our images should end up over here.

And the way we’ll find those images is to count how far the preimages are away from the 𝑦-axis and then do the same for the images. So let’s begin with point 𝐴. 𝐴 is one, two, three, four, five, six, seven, eight.

We could have looked down at the 𝑥-axis to see that 𝐴 was eight to the right on the 𝑥-axis. Therefore, 𝐴 prime should be eight units to the left of the 𝑦-axis. So here would be our 𝐴 prime. And it’s located at negative eight, six.

Now let’s do the same thing for point 𝐵. 𝐵 is also eight units to the right of the 𝑦-axis. So 𝐵 prime should be eight units to the left of the 𝑦-axis. And 𝐵 prime is located at negative eight, one.

Now for point 𝐶, it is two units away from the 𝑦-axis. So 𝐶 prime should be the same, located at negative two, one. 𝐷 is two units away, therefore so is 𝐷 prime. And it is located at negative two, six.

So here would be our image. If we would take the rectangle on the right and reflect it over the 𝑦-axis, we would get the rectangle in the blue.

Therefore, the images of 𝐴𝐵𝐶𝐷 are 𝐴 prime is negative eight, six; 𝐵 prime is negative eight, one; 𝐶 prime is negative two, one; and 𝐷 prime is negative two, six.