Video: Pack 2 • Paper 1 • Question 18

Pack 2 • Paper 1 • Question 18

02:42

Video Transcript

Shape A is shown. Kerrie enlarges shape A by a scale factor of negative two with a center of enlargement zero, zero and calls this shape B. Darius rotates shape A by 180 degrees anticlockwise about negative 1.5, negative 1.5 and calls this shape C. Which coordinate is a vertex of both shape B and shape C?

In order to be able to answer this question, we first have to apply both of the transformations to our shape A. To complete an enlargement about the center zero, zero, we first need to draw our rays. That is, we draw a straight line connecting each vertex with the center of enlargement. Here, the center of enlargement is negative, which means the shape is going to come out of the other side of the center. The vertices of our enlarged shape must lie somewhere along these lines.

Now, we’re given that the scale factor is negative two. This means that the distance from our center to our new shape must be twice the distance from each vertex on the old shape to the center. Let’s start with this one.

To get back to the center of enlargement, we can go three down and three units across. This means that we need to go six units across and six units down to get to the relevant vertex on our enlargement. That’s here.

Now, for this vertex, to get back to the center, we go six down and three across. For our corresponding enlarged vertex then, we need to go six across and 12 down.

Finally, this vertex, we need to go three down and seven across to get back to our center. So to get to the enlarged vertex, we’re going to go 14 across and six down. We now have the vertices of our enlarged triangle B.

The next step is to rotate shape A 180 degrees anticlockwise about negative 1.5, negative 1.5. Tracing paper can be a really useful tool to help us. By tracing shape A onto a piece of tracing paper and putting our pen in the center of rotation, we can see that shape C ends up as shown.

The coordinate that is a vertex of both shape B and shape C is, therefore, negative six, negative six.

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