Question

use the graph and the translation (x,y)→(x + 4,y + 1) to answer parts a and b below. a. enter the image of each vertex as an ordered pair. a→a b→b c→c (type ordered pairs.)

Explanation:

1. First, identify the coordinates of the original vertices:

• From the graph, assume the coordinates of point \(A=(4,6)\), \(B=(2,3)\), and \(C=(0,4)\).
• The translation rule is \((x,y)\to(x + 4,y + 1)\).

1. Calculate the new - coordinates of point \(A\):

• For point \(A=(4,6)\), using the translation rule \((x,y)\to(x + 4,y + 1)\).
• \(x=4\), \(y = 6\).
• The new \(x\) - coordinate is \(x'=4 + 4=8\).
• The new \(y\) - coordinate is \(y'=6 + 1=7\). So, \(A'=(8,7)\).

1. Calculate the new - coordinates of point \(B\):

• For point \(B=(2,3)\), using the translation rule \((x,y)\to(x + 4,y + 1)\).
• \(x = 2\), \(y = 3\).
• The new \(x\) - coordinate is \(x'=2+4 = 6\).
• The new \(y\) - coordinate is \(y'=3 + 1=4\). So, \(B'=(6,4)\).

1. Calculate the new - coordinates of point \(C\):

• For point \(C=(0,4)\), using the translation rule \((x,y)\to(x + 4,y + 1)\).
• \(x = 0\), \(y = 4\).
• The new \(x\) - coordinate is \(x'=0 + 4=4\).
• The new \(y\) - coordinate is \(y'=4 + 1=5\). So, \(C'=(4,5)\).

Answer:

\(A'\): \((8,7)\), \(B'\): \((6,4)\), \(C'\): \((4,5)\)