Question

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

Explanation:

Step1: Identify original coordinates

Original vertices: $D(-5, -8)$, $E(3, -8)$, $F(3, 2)$, $G(-5, 2)$

Step2: Apply translation rule

Translation: $(x+3, y+3)$

• $D'$: $(-5+3, -8+3)=(-2, -5)$
• $E'$: $(3+3, -8+3)=(6, -5)$
• $F'$: $(3+3, 2+3)=(6, 5)$
• $G'$: $(-5+3, 2+3)=(-2, 5)$

Step3: Plot new vertices

Connect $D'(-2, -5)$, $E'(6, -5)$, $F'(6, 5)$, $G'(-2, 5)$ to form the translated rectangle.

Answer:

The translated rectangle has vertices $D'(-2, -5)$, $E'(6, -5)$, $F'(6, 5)$, $G'(-2, 5)$. When plotted and connected, this forms the image of rectangle $DEFG$ after the translation.