Question Video: Determining the Coordinates of Points after Reflection Mathematics • 11th Grade

Video Transcript

Given that line segment 𝐴 prime 𝐵 prime is the image of line segment 𝐴𝐵 by reflection in the 𝑦-axis, find the coordinates of the points 𝐴 prime and 𝐵 prime.

On the graph, we can see that we have the line segment 𝐴𝐵. We are told that this line segment will be reflected in the 𝑦-axis to create the line segment 𝐴 prime 𝐵 prime, which will be the image of the original line segment. And there are a few ways that we can answer this question. However, given that we have a graph already drawn, let’s use that method to begin with.

When we perform a reflection, for example, if we start with point 𝐴, we consider the perpendicular distance from that point to the mirror line. And the reflected point, or the image, will be exactly the same distance away on the opposite side of the mirror line. So this point 𝐴 prime is at the coordinates negative one, three. Now let’s do the same for point 𝐵. It has a perpendicular distance of five units from the mirror line of the 𝑦-axis. And so the image 𝐵 prime will be at a perpendicular distance of five units on the opposite side of the mirror line. It’s at the coordinates negative five, four. We can join the points to create the image, line segment 𝐴 prime 𝐵 prime. And the coordinates 𝐴 prime at negative one, three and 𝐵 prime at negative five, four would be the answer.

But as previously mentioned, there is another method we could use to find these coordinates, which has the advantage of not requiring us to draw out the points on a graph. And that is by recalling that for a general point 𝑃 with coordinates 𝑥, 𝑦, a reflection in the 𝑦-axis maps point 𝑃 to point 𝑃 prime with coordinates negative 𝑥, 𝑦. So, when point 𝐴, which has the coordinates one, three, is reflected, it produces the image 𝐴 prime with coordinates negative one, three. This is because the image has an 𝑥-coordinate, which is the negative of the original 𝑥-coordinate. If the original 𝑥-coordinate was already negative, then the image would have a positive 𝑥-coordinate.

And we can do the same for point 𝐵 with coordinates five, four. Using the same rule, we know that 𝐵 prime will have the coordinates negative five, four, thus confirming the answers for the coordinates of 𝐴 prime and 𝐵 prime that we found previously.