The diagram shows shape A and shape B. Shape A can be mapped to shape B by a single transformation. Josh says that shape A can only be mapped to shape B by reflecting it in the 𝑦-axis. Is Josh correct? Tick the correct box. Yes or no. Then give a reason for your answer.
In this case, Josh is not correct. It is certainly true that shape A reflected over the 𝑦-axis would be shape B. However, there’s another transformation that can get us from A to B. We can get from shape A to shape B by translating shape A seven units to the left.
The reason Josh is not correct is that shape A can also be translated seven units left to give shape B.
Part b) says, “The diagram shows triangles A and B. Triangle A is mapped to triangle B by a combination of two transformations. The first transformation is a reflection in the 𝑥-axis. Fully describe the second transformation.”
Before we describe the second transformation, let’s go ahead and graph the first transformation, a reflection in the 𝑥-axis on our grid. Reflecting over the 𝑥-axis means making the 𝑦-coordinate negative. If we began with the point at negative eight, two, a reflection of the 𝑥-axis changes that to negative eight, negative two. Negative four, two becomes negative four, negative two and negative six, positive six becomes negative six, negative six.
Connecting the dots gives us A prime. The second transformation is what is happening between A prime and B. Triangle A prime has a base of four units, while triangle B has a base of two units. Triangle B is half the size of triangle A prime. And we write that as an enlargement by a scale factor of one-half.
We need to be careful here because anytime we have an enlargement, we’ll also have a centre. The centre is the place where these rays all cross. In our case, we have a centre at the origin. We can call the centre point 𝑂.
To make these rays, we draw lines from corresponding vertices for all three sets of vertices. And their intersection — in this case at the origin — is the centre of your enlargement.