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

`\text{\text{Area of square K'L'M'N'}} = (1)/(25)* \text{Area of square KLMN}`

Explanation:

We are given the following information in the question:

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

Dilation factor =
`\displaystyle(1)/(5)`

We know that:

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

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