Question

draw the image of quadrilateral abcd under a translation by 2 units to the left and 3 units up.

Explanation:

Step1: Recall translation rule

For a translation 2 units left and 3 units up, the rule for a point $(x,y)$ is $(x - 2,y+3)$.

Step2: Translate point A

If the coordinates of point A are $(2,-3)$, then the new - coordinates are $(2 - 2,-3 + 3)=(0,0)$.

Step3: Translate point B

If the coordinates of point B are $(-1,3)$, then the new - coordinates are $(-1 - 2,3 + 3)=(-3,6)$.

Step4: Translate point C

If the coordinates of point C are $(-1,-2)$, then the new - coordinates are $(-1 - 2,-2 + 3)=(-3,1)$.

Step5: Translate point D

If the coordinates of point D are $(-4,-4)$, then the new - coordinates are $(-4 - 2,-4 + 3)=(-6,-1)$.

Step6: Plot new points

Plot the points $(0,0),(-3,6),(-3,1),(-6,-1)$ on the coordinate - plane and connect them in order to form the translated quadrilateral.

Answer:

Plot points $(0,0),(-3,6),(-3,1),(-6,-1)$ and connect them to get the image of quadrilateral $ABCD$.