Question

The length of CD is 12 units C’D’ is the image of CD under a dilation with a scale factor of n.Which of these are true?

Answer 1

Answer: FIrst option, Fourth option and Fifth option.

Step-by-step explanation:

First it is important to know the definition of "Dilation".

A Dilation is defined as a transformation in which the Image (which is the figure obtained after the transformation) and the Pre-Image (this is the original figure, before the transformations) have the same shape, but their sizes are different.

If the length of CD is dilated with a scale factor of "n" and it is centered at the origin, the length C'D' will be:

$C'D'=nCD=(n)(12\ units)$

Therefore, knowing this, you can determine that:

1. If $n=\frac{3}{2}$ , you get:

$C'D'=(\frac{3}{2})(12\ units)=18\ units$

2. If $n=4$, then the length of C'D' is:

$C'D'=(4)(12\ units)=48\ units$

3. If $n=8$, then:

$C'D'=(8)(12\ units)=96\ units$

4. If $n=2$, then, you get that the lenght of C'D' is:

$C'D'=(2)(12\ units)=24\ units$

5. If $n=\frac{3}{4}$, the length of C'D' is the following:

$C'D'=(\frac{3}{4})(12\ units)=9\ units$