Question

draw the image of quadrilateral abcd under a translation by 2 units to the right and 5 units down.

Explanation:

Step1: Recall translation rule

For a point $(x,y)$ translated 2 units to the right and 5 units down, the new - point $(x',y')$ has coordinates $x'=x + 2$ and $y'=y-5$.

Step2: Find new coordinates of point A

Suppose the coordinates of point A are $(x_A,y_A)$. If $x_A=-4$ and $y_A = 1$, then $x_A'=-4 + 2=-2$ and $y_A'=1-5=-4$.

Step3: Find new coordinates of point B

Suppose the coordinates of point B are $(x_B,y_B)$. If $x_B = 3$ and $y_B=-1$, then $x_B'=3 + 2=5$ and $y_B'=-1-5=-6$.

Step4: Find new coordinates of point C

Suppose the coordinates of point C are $(x_C,y_C)$. If $x_C = 2$ and $y_C = 2$, then $x_C'=2 + 2=4$ and $y_C'=2-5=-3$.

Step5: Find new coordinates of point D

Suppose the coordinates of point D are $(x_D,y_D)$. If $x_D=-5$ and $y_D = 3$, then $x_D'=-5 + 2=-3$ and $y_D'=3-5=-2$.

Step6: Plot the new quadrilateral

Plot the points $A'(-2,-4)$, $B'(5,-6)$, $C'(4,-3)$ and $D'(-3,-2)$ on the coordinate - plane and connect them in order to get the image of quadrilateral ABCD under the given translation.

Answer:

Plot points $A'(-2,-4)$, $B'(5,-6)$, $C'(4,-3)$ and $D'(-3,-2)$ and connect them to form the translated quadrilateral.