Question

draw the image of quadrilateral abcd under the translation (x,y)→(x - 7,y + 1).

Explanation:

Step1: Recall translation rule

The translation rule is $(x,y)\to(x - 7,y + 1)$. This means we subtract 7 from the $x$-coordinate and add 1 to the $y$-coordinate of each vertex.

Step2: Find new coordinates of point A

Suppose the coordinates of point A are $(x_A,y_A)$. The new coordinates $A'$ will be $(x_A-7,y_A + 1)$.

Step3: Find new coordinates of point B

Suppose the coordinates of point B are $(x_B,y_B)$. The new coordinates $B'$ will be $(x_B-7,y_B + 1)$.

Step4: Find new coordinates of point C

Suppose the coordinates of point C are $(x_C,y_C)$. The new coordinates $C'$ will be $(x_C-7,y_C + 1)$.

Step5: Find new coordinates of point D

Suppose the coordinates of point D are $(x_D,y_D)$. The new coordinates $D'$ will be $(x_D-7,y_D + 1)$.

Step6: Plot the new points

Plot the new points $A'$, $B'$, $C'$, and $D'$ on the coordinate - plane and connect them in order to form the translated quadrilateral.

Since the original coordinates of $A$, $B$, $C$, and $D$ are not given in numerical values in the problem - statement, the general procedure for the translation is as above. To actually draw the image, you would need to know the specific coordinates of the vertices of the quadrilateral $ABCD$ and perform the arithmetic operations on the coordinates to get the new vertices and then plot them.

Answer:

Follow the steps above to find the new vertices and draw the translated quadrilateral. If the coordinates of $A$, $B$, $C$, and $D$ are known, calculate the new coordinates using $(x,y)\to(x - 7,y + 1)$ and plot the new points.