If a two-dimensional shape is dilated by a factor of 1/3 , what is the effect on the area?

Answer 1

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

In this case, the factor of dilation is \(k = \frac{1}{3}\). Therefore, the area will be multiplied by \(k^2 = \left(\frac{1}{3}\right)^2 = \frac{1}{9}\).

So, when a two-dimensional shape is dilated by a factor of \(\frac{1}{3}\), the new area will be \(\frac{1}{9}\) times the original area.