Question

quadrilateral abcd is the image of quadrilateral abcd under a rotation 90° counterclockwise about the origin followed by a translation.
write the rules for the rotation and translation.
rotation: (x, y) ↦ ( , )
translation: (x, y) ↦ ( , )

Explanation:

Step1: Recall the rotation rule

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

Step2: Find the translation rule

Let's take a point, say \(A(4,0)\). After rotation \(90^{\circ}\) counter - clockwise about the origin, \(A\) becomes \(A_1(0,4)\). The final image of \(A\) is \(A'(0,0)\). To get from \((0,4)\) to \((0,0)\), we subtract \(4\) from the \(y\) - coordinate. So the translation rule is \((x,y)\to(x,y - 4)\).

Answer:

Rotation: \((x,y)\to(-y,x)\)
Translation: \((x,y)\to(x,y - 4)\)