Question

Can anyone help me with a quick question?
Polygon ABCD is dilated by a scale factor of 1.5 with point A as the center of dilation, resulting in the image A'B'C'D'. If the length of is 4.5 units, which sentence about is true?

Answer 1

Options:
The length of is 4.5 units, but does not pass through A.

The length of is 6.75 units, and passes through A.

The length of is 6.75 units, but does not pass through A.

The length of is 9.0 units, and passes through A.

The length of is 9.0 units, but does not pass through A.

Answer 2

I assume it means If the length [of ABCD] is 4.5.
Then with a dilation with scale factor 2, the lengths of sides are multiplied by 2. However, since A is the center of dilation, the image cannot pass through A.

Answer 3

@anthonyym I am so sorry, it is if the lenght of CD is 4.5 then what is the lenght of C´D´

Answer 4

That's alright. The length of C'D' (the afterimage) will be twice the preimage because you are dilating (stretching) the preimage by a scale factor of 2 - the sides are multiplied by 2.

Answer 5

And it will not pass through A because A is the center of dilation. Each point in the afterimage will be twice the distance from the center of dilation and so points won't pass through A.

Answer 6

So the lenght would be 6.75?

Answer 7

@anthonyym

Answer 8

How did you get 6.75