Question

write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Identify original coordinates

Assume original coordinates of \(E=(6,9)\), \(F=(10,9)\), \(G=(10,4)\), \(H=(6,4)\). The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(y, - x)\).

Step2: Rotate point E

For point \(E(6,9)\), applying the rule \((x,y)\to(y, - x)\), we get \(E'=(9,-6)\).

Step3: Rotate point F

For point \(F(10,9)\), applying the rule \((x,y)\to(y, - x)\), we get \(F'=(9,-10)\).

Step4: Rotate point G

For point \(G(10,4)\), applying the rule \((x,y)\to(y, - x)\), we get \(G'=(4,-10)\).

Step5: Rotate point H

For point \(H(6,4)\), applying the rule \((x,y)\to(y, - x)\), we get \(H'=(4,-6)\).

Answer:

The new coordinates are \(E'=(9,-6)\), \(F'=(9,-10)\), \(G'=(4,-10)\), \(H'=(4,-6)\)