Question

If Figure A is multiplied by a scale factor of .5, reflected over the x-axis, and translated 3 units left and 8 units down, which is true about A′?

Answer 1

Answer:

A' has the same shape but not the same size as Figure A.

Step-by-step explanation:

Answer 2

Answer:

A1 has the same shape but not the same size as Figure A.

Step-by-step explanation:

Let's imagine this in our heads:

1. Figure A is multiply by a scale factor of 0.5

Remember when you learned about similarity? Similar figures have a scale factor between them, so the shape that you have at this step is similar to the original.

2. Reflected over the x-axis.

Remember reflection? Reflection is a congruence transformation: the product of a reflection is the same shape and size as the original. Therefore, the figure stays the same at this step, just reflected over the x-axis.

3. Translated 3 units left and 8 units down.

Translation is a congruence transformation as well. The location of the figure will change, but the size and shape will not.

So, the end result is a figure that is similar to the original, and has a scale factor of 0.5 with the original.

This means that it is smaller than the original shape: so we can rule out the first option.

A reflection across the x-axis means that the resulting figure will be on the opposite side of it. Since the original shape is above the x axis, the resulting figure after a reflection will be below. We can rule out the second option.

Now, we get to the third one. A1 has the same shape but not the same size as Figure A. This is true. That is the definition of similar triangles, and we know that triangles A and A1 share a scale factor of 0.5

Hope this helps :)