Chapter 11.4, Problem 15IP

To determine

To find the missing coordinates and the translation of $\Delta RST$ onto $\Delta R\text{'}S\text{'}T\text{'}$ .

Answer to Problem 15IP

  $S\text{'}(-14,2)$

  $T\text{'}(0,9)$

Explanation of Solution

Given:

  $\Delta RST$ where $R(4,2)$ , $S(-8,0)$ and $T(6,7)$ .

After translation $R\text{'}$ has coordinates $(-2,4)$

Concept used:

In the process of translation, to translate a given point say $Q(x,y)$ the following methods are used:

To move $a$ units in horizontal direction, add $a$ to the $x$ coordinate for right direction and subtract $a$ from $x$ coordinate for left direction.

To move $a$ units in vertical direction, add $a$ to the $y$ coordinate for upward direction and subtract $a$ from $y$ coordinate for downward direction.

Calculation:

According to the question, $R(4,2)$ is translated to $R\text{'}(-2,4)$ .

This is possible when $\Delta RST$ is translated 4 units to the left and 2 units up.

Therefore,

Coordinates of vertices of $\Delta RST$	Coordinates of vertices of $\Delta R\text{'}S\text{'}T\text{'}$
$R(4,2)$	$R\text{'}(-2,4)$
$S(-8,0)$	$S\text{'}(-14,2)$
$T(6,7)$	$T\text{'}(0,9)$

Graph:

  

Interpretation:

The graph shows the original figure as well as the image after translation.

Conclusion:

Therefore, the $\Delta RST$ is translated to 6 units to the left and 2 units up to obtain $\Delta R\text{'}S\text{'}T\text{'}$ .