Question

If a two-dimensional shape is dilated by a factor of 13
1
3
, what is the effect on the area?(1 point)
Responses

It is 16
1
6
as great.
It is Start Fraction 1 over 6 End Fraction as great.

It is 19
1
9
as great.
It is Start Fraction 1 over 9 End Fraction as great.

It is 13
1
3
as great.
It is Start Fraction 1 over 3 End Fraction as great.

It is 23
2
3
as great.
It is Start Fraction 2 over 3 End Fraction as great.

Answer 1

When a two-dimensional shape is dilated by a factor of \( k \), the area of the shape is multiplied by \( k^2 \).

In this case, the dilation factor is \( \frac{1}{3} \). To find the effect on the area, we calculate:

\[
\text{New Area} = \text{Original Area} \times \left(\frac{1}{3}\right)^2 = \text{Original Area} \times \frac{1}{9}
\]

This means the new area is \( \frac{1}{9} \) as great as the original area.

Thus, the correct response is:

**It is \( \frac{1}{9} \) as great.**