Chapter 12.7, Problem 14E

To determine

To find whether the image will be smaller than, larger than or congruent to the original figure after dilation.

Answer to Problem 14E

The image will be greater than the original figure when the scale factor is $\text{3}$ .

The image will be smaller than the original figure when the scale factor is $\text{0}\text{.5}$ .

The image will be congruent to the original figure when the scale factor is $\text{1}$ .

Explanation of Solution

Given information:

The scale factors are $\text{3,0}\text{.5 and 1}$

Calculation :

The coordinates after dilation with scale factor $\text{3}$ will be:

  $\left(\text{x,y}\right)\to \left(\text{3x,3y}\right)$

Hence, the image will be greater than the original figure when the scale factor is $\text{3}$ .

The coordinates after dilation with a scale factor $\text{0}\text{.5}$ will be:

  $\left(\text{x,y}\right)\to \left(\text{0}\text{.5x,0}\text{.5y}\right)$

Hence, the image will be smaller than the original figure when the scale factor is $\text{0}\text{.5}$ .

The coordinates after dilation with scale factor $\text{1}$ will be:

  $\left(\text{x,y}\right)\to \left(\text{x,y}\right)$

Hence, the image will be congruent to the original figure when the scale factor is $\text{1}$ .