Question

Given the pre-image ABCD and the image after a dilation, A'B'C'D', what is true about the polygons? Check all that apply. The length AB is 2. The length A'B' is 3. The image is smaller than the pre-image. The scale factor is . The scale factor is .

Answer 1

The answer is 1.5 i believe

Answer 2

Answer

You should check the following:

The length of AB is 2

The length of A'B' is 3

The scale factor is $\frac{3}{2}$

Explanation

- To find the length of AB, we will use the distance formula:

$d(A,B)=|x_{1}-x_{2}|$

From the picture we can infer that $x_{1}=2$ and $x_{2}=4$, so let's replace the values.

$d(A,B)=|2-4|$

$d(A,B)=|-2|$

$d(A,B)=2$

The length of AB is 2, so you should check the first answer

- To find the length of A'B', we will use the distance formula one more time:

From the picture we can infer that $x_{1}=3$ and $x_{2}=6$, so let's replace the values.

$d(A',B')=|3-6|$

$d(A',B')=|-3|$

$d(A',B')=3$

Since the length of A'B' is 3, you should also check the second answer as well.

- In a transformation (in this case a dilation) the pre-image is the original shape and the image is the shape after the transformation.

Since the image is bigger than the pre-image, the third answer is false.

- Let $k$ be the scale factor

We know that the length of AB is 2 and we need to multiply that length by the scale factor to get length of A'B' i.e 3, so:

$2k=3$

$k=\frac{3}{2}$

Since the scale factor is $\frac{3}{2}$, you should check the fourth answer as well.

- We already prove that the scale factor is $\frac{3}{2}$, so the fifth answer is false.