Question

use the graph and the translation $(x,y)\to(x + 3,y - 4)$ 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

Assume the original coordinates of \(R\), \(S\), \(T\), \(V\) from the graph. Let's say \(R=(x_1,y_1)\), \(S=(x_2,y_2)\), \(T=(x_3,y_3)\), \(V=(x_4,y_4)\). Suppose \(R=( - 1,1)\), \(S=( - 3,5)\), \(T=(1,7)\), \(V=(3,3)\) (coordinates are assumed based on a standard grid - you need to accurately read from the given graph).

Step2: Apply the translation rule \((x,y)\to(x + 3,y-4)\)

For point \(R\):
\(x=-1\), \(y = 1\). After translation, \(x'=-1 + 3=2\), \(y'=1-4=-3\). So \(R\to(2,-3)\)
For point \(S\):
\(x=-3\), \(y = 5\). After translation, \(x'=-3 + 3=0\), \(y'=5-4 = 1\). So \(S\to(0,1)\)
For point \(T\):
\(x=1\), \(y = 7\). After translation, \(x'=1+3 = 4\), \(y'=7 - 4=3\). So \(T\to(4,3)\)
For point \(V\):
\(x=3\), \(y = 3\). After translation, \(x'=3+3=6\), \(y'=3-4=-1\). So \(V\to(6,-1)\)

Answer:

\(R\to(2,-3)\), \(S\to(0,1)\), \(T\to(4,3)\), \(V\to(6,-1)\)