Question

draw the following quadrilateral after a translation 4 units to the left and 4 units down.

Explanation:

Step1: Recall translation rule

For a translation $4$ units to the left and $4$ units down, the rule for a point $(x,y)$ is $(x - 4,y - 4)$.

Step2: Identify vertices of original quadrilateral

Suppose the vertices of the original quadrilateral are $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$.

Step3: Apply translation rule to each vertex

The new vertices will be $(x_1 - 4,y_1 - 4),(x_2 - 4,y_2 - 4),(x_3 - 4,y_3 - 4),(x_4 - 4,y_4 - 4)$.

Step4: Plot new quadrilateral

Plot the new - found vertices on the coordinate plane and connect them to form the translated quadrilateral.

Answer:

Plot the quadrilateral with vertices obtained by applying the rule $(x,y)\to(x - 4,y - 4)$ to the original quadrilateral's vertices.