Video Transcript
What is the image of the point negative eight, 10 reflected in the 𝑦-axis?
We’re asked to determine the coordinates of the image of a given point following a reflection in the 𝑦-axis. Let’s start by visualizing this transformation on a sketch of a coordinate grid.
Reflecting an object in the 𝑦-axis has a horizontal effect. The point appears on the opposite side of the 𝑦-axis, but the same horizontal distance away. The vertical height, and hence the 𝑦-coordinate, of the point is unchanged, but its 𝑥-coordinate changes sign as it swaps from either the negative to positive or positive to negative part of the 𝑥-axis. The image of the point negative eight, 10 will therefore be the point eight, 10.
We can also recall the general result that a reflection in the 𝑦-axis maps a point 𝑃 with coordinates 𝑥, 𝑦 to the point 𝑃 prime with coordinates negative 𝑥, 𝑦. The 𝑦-coordinate is unchanged, but the 𝑥-coordinate changes sign, as we’ve already seen. Applying this mapping to the point negative eight, 10 gives the coordinates of its image as negative one multiplied by negative eight, 10. Negative one multiplied by negative eight is positive eight.
So both visually and using the general mapping rule, we’ve shown that the image of the point negative eight, 10 following a reflection in the 𝑦-axis is the point eight, 10.
