Question

Which graph shows a dilation?

Answer 1

Answer:

Option A is the correct choice.

Step-by-step explanation:

We have been given four graphs. We are asked to choose the graph that represents a dilation.

We know that dilation is a transformation that produces an image similar to pre-image (original), but with a different size.

• When the new image is larger than original figure that it is an enlargement, which means scale factor is greater than 1.

• When the new image is smaller than original figure that it is a reduction, which means scale factor is less than 1.

Since dilation preserve orientation, so each pair of figures must stay in the same order.

Upon looking at our given graphs, we can see that in the graphs B, C and D the size and shape of each pair of given figures is different.

The pairs represented in graphs B, C and D don't preserve orientation, therefore, these are not correct choices.

Upon looking at graph A, we can see that the given pair of figures have same orientation, same shape and one figure is bigger than another, therefore, option A is the correct choice.

Answer 2

Answer: The correct graph is the first one. Attached below.

Step-by-step explanation:  We are given to select the graph that shows dilation.

DILATION:  A dilation stretches or shrinks the original figure. it includes the scale factor and the centre of the dilation. The centre of dilation is a fixed point in the plane.

Also, If the scale factor is greater than 1, the image is an enlargement and if it is less than 1, it is a reduction.

The original and the dilated images have same shapes but different sizes.

We can see that in the graphs 2, 3 and 4, the pairs of figures do not have same shapes. So, they cannot show dilation.

The graph 1 includes the figures having same shapes and different sizes.

So, the graph 1 will show dilation.

We can see that the length of a side of the smaller figure is 2 units and the length of the corresponding side of the larger figure is 6 units.

Therefore, if larger figure is dilated to smaller one, then scale factor will be

$S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}=\dfrac{2}{6}=\dfrac{1}{3}$

In this case, the dilation is a reduction.

If smaller figure is dilated to larger one, then scale factor will be

$S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}=\dfrac{6}{2}=3>1.$

In this case, the dilation is an enlargement.

The correct graph (first one) is shown in the attached picture.