Chapter 12.4, Problem 18E

To determine

To draw: The image of the rectangle after the given translation.

Answer to Problem 18E

The image after translation will be as follows:

  $A\text{'}B\text{'}C\text{'}D\text{'}$ is the image.

Explanation of Solution

Given information:

The following rectangle:

To make the translation $4$ units left and $2$ units up, subtract $4$ units from $x$ coordinate and add $2$ units to the $y$ coordinate. Plot the given figure anywhere on the graph. Assume the vertices to be $ABCD$ . Assume the coordinates as:

$A(1,1),B(4,1),C(4,3),D(1,3)$

( $AB$ and $CD$ should be of $4$ units. $BC$ and $AD$ should be of $2$ units)

To make translation subtract $4$ units from $x$ coordinate and add $2$ units to the $y$ coordinate of the above given vertices. The vertices of the image will be:

$A\text{'}(-3,3),B\text{'}(0,3),C\text{'}(0,5),D\text{'}(-3,5)$

The image after translation will be as follows:

  $ABCD$ is the original figure.

  $A\text{'}B\text{'}C\text{'}D\text{'}$ is the image.