Question

use the graph and the translation (x,y)→(x + 5,y + 4) 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:

Step1: Identify original coordinates

Assume \(A=(x_1,y_1)\), \(B=(x_2,y_2)\), \(C=(x_3,y_3)\) from the graph. Let's say \(A = (-2,5)\), \(B=(1,3)\), \(C=( - 1,-3)\) (you need to accurately read from the graph).

Step2: Apply the translation rule \((x,y)\to(x + 5,y+4)\) to point A

For point \(A(-2,5)\), \(x=-2,y = 5\). New \(x=-2 + 5=3\), new \(y=5 + 4 = 9\). So \(A'\) is \((3,9)\).

Step3: Apply the translation rule to point B

For point \(B(1,3)\), \(x = 1,y=3\). New \(x=1+5 = 6\), new \(y=3 + 4=7\). So \(B'\) is \((6,7)\).

Step4: Apply the translation rule to point C

For point \(C(-1,-3)\), \(x=-1,y=-3\). New \(x=-1 + 5=4\), new \(y=-3 + 4 = 1\). So \(C'\) is \((4,1)\).

Answer:

\(A\to A'(3,9)\)
\(B\to B'(6,7)\)
\(C\to C'(4,1)\)