Question

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

Explanation:

Step1: Identify original coordinates

Assume \(D(-6,-8)\), \(E(2,-8)\), \(F(2,2)\), \(G(-6,2)\)

Step2: Apply translation rule

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

Step3: Graph new rectangle

Plot the new points \((-3,-5)\), \((5,-5)\), \((5,5)\), \((-3,5)\) and connect them to form the new rectangle.

Answer:

Graph the rectangle with vertices \((-3,-5)\), \((5,-5)\), \((5,5)\), \((-3,5)\)