Video Transcript
A transformation is applied to the triangle with vertices 𝐴: 𝑥, 𝑦; 𝐵: 𝑥, 𝑦 plus two; 𝐶: 𝑥 plus two, 𝑦. The image has vertices 𝐴 prime which is negative 𝑥, negative 𝑦; 𝐵 prime is negative 𝑥, negative 𝑦 minus two; 𝐶 prime is negative 𝑥 minus two, negative 𝑦. Which of the following transformations has taken place? Is it (A) a rotation, (B) a reflection, or (C) a translation?
Let’s look at each vertex in turn. If we compare vertex 𝐴 with its image 𝐴 prime, we see that we’re mapping coordinates 𝑥, 𝑦 onto the coordinate negative 𝑥, negative 𝑦. Then, when we look at vertex 𝐵, we’re mapping 𝑥, 𝑦 plus two onto negative 𝑥, negative 𝑦 minus two. Finally, vertex 𝐶 maps from 𝑥 plus two, 𝑦 onto negative 𝑥 minus two, negative 𝑦. Can we spot a common theme here?
Let’s imagine we had vertices 𝑎, 𝑏. We can see that the signs of both the 𝑥-part and the 𝑦-part has changed, so 𝑎, 𝑏 would map onto negative 𝑎, negative 𝑏. So, what transformation causes this? At first glance, it might feel like this needs to be a reflection. But in fact, this won’t quite give us the correct coordinates. And instead, we need to recall that a rotation of 180 degrees about the origin, the point zero, zero, does indeed map a coordinate 𝑎, 𝑏 onto a point with coordinates negative 𝑎, negative 𝑏. And so the correct answer here must be (A); it’s a rotation.
