Chapter 11.4, Problem 4IP

To determine

To find he coordinates of the image of a given triangle after translation.

Explanation of Solution

Given:

  $\Delta XYZ$ with $X(0,4)$, $Y(-2,0)$, $Z(2,0)$.

  

Calculation for graph:

Consider the image of the $\Delta XYZ$ as $\Delta X\text{'}Y\text{'}Z\text{'}.$

The image formed by the $\Delta XYZ$ with $X(0,4)$, $Y(-2,0)$, $Z(2,0)$ can be represented as,

  

Now, shift or translate the figure $2$ unit right and $3$ unit up.

Now, finding the coordinates of the vertices by observing the graph of the original triangle after translation.

Coordinates of $\Delta XYZ$	Coordinates of $\Delta X\text{'}Y\text{'}Z\text{'}$
$X(0,4)$	$X\text{'}(-2-1)$
$Y(-2,0)$	$Y\text{'}(4,3)$
$Z(2,0)$	$Z\text{'}(0,3)$

Graph:

  

Interpretation:

In the above graph, the shaded portion shows $\Delta X\text{'}Y\text{'}Z\text{'}$ .