Question

given the graph of \\( \delta efg \\), find the coordinates of the \\( \delta efg \\)

• \\( (x,y)\to(x + 2,y + 3) \\) followed by reflection about the \\( y \\)-axis

\\( e(\square,\square) \\)
\\( f(\square,\square) \\)
\\( g(\square,\square) \\)

Explanation:

Step1: Find the original coordinates

From the graph, \(E=(0,0)\), \(F=(3,1)\), \(G=(2, - 2)\)

Step2: Apply the translation \((x,y)\to(x + 2,y+3)\)

For point \(E\):
\(x=0+2 = 2\), \(y=0 + 3=3\), so \(E'=(2,3)\)
For point \(F\):
\(x=3+2=5\), \(y=1 + 3=4\), so \(F'=(5,4)\)
For point \(G\):
\(x=2+2=4\), \(y=-2 + 3=1\), so \(G'=(4,1)\)

Step3: Apply the reflection about the \(y\) - axis \((x,y)\to(-x,y)\)

For point \(E'\):
\(x=-2\), \(y = 3\), so \(E''=(-2,3)\)
For point \(F'\):
\(x=-5\), \(y = 4\), so \(F''=(-5,4)\)
For point \(G'\):
\(x=-4\), \(y = 1\), so \(G''=(-4,1)\)

Answer:

\(E''(-2,3)\), \(F''(-5,4)\), \(G''(-4,1)\)