Question

graph the image of rectangle defg after a translation 3 units right and 3 units up.

Explanation:

Step1: Find the coordinates of original points

Assume \(D(-5,-8)\), \(E(3,-8)\), \(F(3,2)\), \(G(-5,2)\)

Step2: Apply the translation rule

The translation rule for 3 units right (\(x\) - coordinate \(+3\)) and 3 units up (\(y\) - coordinate \(+3\)) is \((x,y)\to(x + 3,y+3)\)
For point \(D(-5,-8)\):
\(x=-5+3=-2\), \(y=-8 + 3=-5\), new point \(D'(-2,-5)\)
For point \(E(3,-8)\):
\(x=3+3=6\), \(y=-8 + 3=-5\), new point \(E'(6,-5)\)
For point \(F(3,2)\):
\(x=3+3=6\), \(y=2+3=5\), new point \(F'(6,5)\)
For point \(G(-5,2)\):
\(x=-5+3=-2\), \(y=2+3=5\), new point \(G'(-2,5)\)

Step3: Plot the new points

Plot \(D'(-2,-5)\), \(E'(6,-5)\), \(F'(6,5)\), \(G'(-2,5)\) on the coordinate plane and connect them to form the translated rectangle.

Answer:

Plot the points \(D'(-2,-5)\), \(E'(6,-5)\), \(F'(6,5)\), \(G'(-2,5)\) and connect them.