Question

use the graph and the translation $(x,y)\to(x + 2,y - 1)$ to answer parts a and b below.
a. enter the image of each vertex as an ordered pair.
$r\to r\square$ (type an ordered pair.)
$s\to s\square$ (type an ordered pair.)
$t\to t\square$ (type an ordered pair.)
$v\to v\square$ (type an ordered pair.)

Explanation:

Step1: Find the original coordinates

From the graph, assume \( R=(5,1) \), \( S=(3, - 1) \), \( T=(1,3) \), \( V=( - 1,1) \)

Step2: Apply the translation rule \((x,y)\to(x + 2,y-1)\)

For point \( R=(5,1) \):
\(x=5,y = 1\)
\(x+2=5 + 2=7\)
\(y-1=1-1 = 0\)
So \( R'=(7,0) \)
For point \( S=(3,-1) \):
\(x = 3,y=-1\)
\(x + 2=3+2=5\)
\(y-1=-1-1=-2\)
So \( S'=(5,-2) \)
For point \( T=(1,3) \):
\(x = 1,y = 3\)
\(x+2=1+2=3\)
\(y-1=3-1=2\)
So \( T'=(3,2) \)
For point \( V=(-1,1) \):
\(x=-1,y = 1\)
\(x+2=-1+2=1\)
\(y-1=1-1=0\)
So \( V'=(1,0) \)

Answer:

\(R\to R'(7,0)\)
\(S\to S'(5,-2)\)
\(T\to T'(3,2)\)
\(V\to V'(1,0)\)