Answer
You should check the following:
The length of AB is 2
The length of A'B' is 3
The scale factor is [tex]\frac{3}{2}[/tex]
Explanation
- To find the length of AB, we will use the distance formula:
[tex]d(A,B)=|x_{1}-x_{2}|[/tex]
From the picture we can infer that [tex]x_{1}=2[/tex] and [tex]x_{2}=4[/tex], so let's replace the values.
[tex]d(A,B)=|2-4|[/tex]
[tex]d(A,B)=|-2|[/tex]
[tex]d(A,B)=2[/tex]
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 [tex]x_{1}=3[/tex] and [tex]x_{2}=6[/tex], so let's replace the values.
[tex]d(A',B')=|3-6|[/tex]
[tex]d(A',B')=|-3|[/tex]
[tex]d(A',B')=3[/tex]
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 [tex]k[/tex] 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:
[tex]2k=3[/tex]
[tex]k=\frac{3}{2}[/tex]
Since the scale factor is [tex]\frac{3}{2}[/tex], you should check the fourth answer as well.
- We already prove that the scale factor is [tex]\frac{3}{2}[/tex], so the fifth answer is false.
