Question

Square A′B′C′D′ is a dilation of square ABCD .

Answer 1

$\boxed{k=\frac{1}{3}}$

Explanation:

If you want to dilate an object you just need to enlarge or reduce the size of that object. In this way, the scale factor determines how much larger or smaller the object will become. So we know some facts:

• If this factor is greater than 1, the object will increase in size.

• if the factor is less than 1, the object will decrease in size.

One important thing is that the dilated object will be similar to its original. The missing figure is attached below. As you can see, when applying dilation the square ABCD is reduced in size to become the square A'B'C'D', thus the scale factor can be calculated as:

$k=\frac{2}{6}= \\ \\ \therefore \boxed{k=\frac{1}{3}}$

As you can see the factor is less than 1, so the object will decrease in size as we predicted.