Question

If square KLMN is dilated by a scale factor of 1 5 with a center of dilation at the origin, how does the area of K'L'M'N' compare with the area of KLMN?

Answer 1

The  areas will be in the ratio  1 : 1.5^2  = 1 .2.25
The area will be larger by a factor 2.25.

Answer 2

Answer:

$\text{\text{Area of square K'L'M'N'}} = \frac{1}{25}\times \text{Area of square KLMN}$

Step-by-step explanation:

We are given the following information in the question:

The square KLMN is dilated to square K'L'M'N'  .

Dilation factor = $\displaystyle\frac{1}{5}$

We know that:

$\text{(Dilation factor)}^2 = \displaystyle\frac{\text{Area of square K'L'M'N'}}{\text{Area of square KLMN}}\\\\(\frac{1}{5})^2 = \displaystyle\frac{\text{Area of square K'L'M'N'}}{\text{Area of square KLMN}}\\\\\frac{1}{25} = \displaystyle\frac{\text{Area of square K'L'M'N'}}{\text{Area of square KLMN}}\\\\\text{\text{Area of square K'L'M'N'}} = \frac{1}{25}\times \text{Area of square KLMN}$

Hence, the area of square K'L'M'N' is 25 times smaller than the area of square.