Chapter 12.7, Problem 17E

a.

To determine

To draw a triangle DEF and find the vertices of the image after dilation.

Answer to Problem 17E

The coordinates of the vertices after dilation are $\text{D'}\left(10,-2\right)\text{,E'}\left(10,-6\right)\text{ and F'}\left(2,-2\right)$

The triangle is drawn below:

  

Explanation of Solution

Given information:

The coordinates of the triangle DEF are:

  $\text{D}\left(-5,1\right)\text{,E}\left(-5,3\right)\text{ and F}\left(-1,1\right)$

The coordinates are dilated by $\left(\text{x,y}\right)\to \left(-2\text{x},-2\text{y}\right)$ .

Calculation :

The triangle is drawn below:

  

The coordinates of the vertices after dilation by $\left(\text{x,y}\right)\to \left(-2\text{x},-2\text{y}\right)$ are:

  $\begin{array}{l}\text{D}\left(-5,1\right)\to \left(10,-2\right)\\ \text{E}\left(-5,3\right)\to \left(10,-6\right)\\ \text{F}\left(-1,1\right)\to \left(2,-2\right)\end{array}$

The coordinates of the vertices after dilation are $\text{D'}\left(10,-2\right)\text{,E'}\left(10,-6\right)\text{ and F'}\left(2,-2\right)$

The triangle is drawn below:

  

b.

To determine

To find the coordinates after dilation and draw the triangle.

Answer to Problem 17E

The coordinates of the vertices after dilation are $\text{D"}\left(-10,2\right)\text{,E"}\left(-10,6\right)\text{ and F"}\left(-2,2\right)$

The triangle is drawn below:

  

Explanation of Solution

Given information:

The coordinates of the triangle DEF are:

  $\text{D}\left(-5,1\right)\text{,E}\left(-5,3\right)\text{ and F}\left(-1,1\right)$

The coordinates are dilated by $\left(\text{x,y}\right)\to \left(2\text{x},2\text{y}\right)$ .

Calculation :

The coordinates of the vertices after dilation by $\left(\text{x,y}\right)\to \left(2\text{x},2\text{y}\right)$ are:

  $\begin{array}{l}\text{D}\left(-5,1\right)\to \left(-10,2\right)\\ \text{E}\left(-5,3\right)\to \left(-10,6\right)\\ \text{F}\left(-1,1\right)\to \left(-2,2\right)\end{array}$

The coordinates of the vertices after dilation are $\text{D"}\left(-10,2\right)\text{,E"}\left(-10,6\right)\text{ and F"}\left(-2,2\right)$

The triangle is drawn below:

  

c.

To determine

To compare the images formed above.

Answer to Problem 17E

The triangles formed are congruent.

Explanation of Solution

Given information:

The following images were formed:

  

Conclusion :

The triangles formed are congruent, all the sides are equal.