Chapter 12.4, Problem 5E

To determine

To draw the triangle with the given vertices. To find the coordinates of the vertices of the image after the translation and draw the image.

Answer to Problem 5E

The triangle $\text{DEF}$ and its image $\text{D'E'F'}$ can be represented on a graph as:

Explanation of Solution

Given information:

The coordinates of triangle $\text{DEF}$ provided in the question:

$\text{D(-1,-6)},\text{ E(-2,4)},\text{ F(3,-2)}$

The provided coordinate notation for translation:

$(x,y)\to (x-2,y-1)$

As per the problem

Consider the vertices of the triangle $\text{DEF}$ :

  $\text{D(-1,-6)},\text{ E(-2,4)},\text{ F(3,-2)}$

The triangle $\text{DEF}$ can be drawn as follows:

To translatetriangle $\text{DEF}$ , consider the coordinate notation:

  $(x,y)\to (x-2,y-1)$

Subtract $2$ from the $x$ coordinate and $1$ fromthe $y$ coordinate of each vertex

Original Image

$(x,y)\to (x-2,y-1)$

$\text{D(-1,-6)}\to \text{D'(-3,-7)}$

$\text{ E(-2,4)}\to \text{E'(-4,3)}$

  $\text{ F(3,-2)}\to \text{F'(1,-3)}$

The image $\text{D'E'F'}$ using the above coordinates will be as follows:

Conclusion: The image $\text{D'E'F'}$ has moved $2$ unit to the left and $1$ units down from the original triangle $\text{DEF}$ .