Question

which shows the image of quadrilateral abcd after the transformation r0, 90°?

Explanation:

Step1: Recall rotation rule

The rule for a $90^{\circ}$ counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.

Step2: Apply rule to vertices

For each vertex of the quadrilateral, substitute the $x$ and $y$ coordinates into the rotation rule.

Step3: Plot new vertices

Use the new coordinates of the vertices to draw the image of the quadrilateral.

Answer:

To find the image of a point $(x,y)$ after a $90^{\circ}$ counter - clockwise rotation about the origin $R_{0,90^{\circ}}$, we use the transformation rule $(x,y)\to(-y,x)$.
Let's assume the coordinates of the vertices of quadrilateral $ABCD$ are $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$ and $D(x_4,y_4)$.
For vertex $A$: If $A=(x_1,y_1)$, then $A'=(-y_1,x_1)$ after the $90^{\circ}$ counter - clockwise rotation about the origin.
For vertex $B$: If $B=(x_2,y_2)$, then $B'=(-y_2,x_2)$ after the $90^{\circ}$ counter - clockwise rotation about the origin.
For vertex $C$: If $C=(x_3,y_3)$, then $C'=(-y_3,x_3)$ after the $90^{\circ}$ counter - clockwise rotation about the origin.
For vertex $D$: If $D=(x_4,y_4)$, then $D'=(-y_4,x_4)$ after the $90^{\circ}$ counter - clockwise rotation about the origin.
Plot the new points $A'$, $B'$, $C'$ and $D'$ to get the image of the quadrilateral $ABCD$.