Question

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

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(270^{\circ}\) counter - clockwise around the origin, the new coordinates \((x',y')\) follow the rule \((x,y)\to(y, - x)\)

Step2: Find coordinates of \(E(1,-4)\)

For point \(E(1,-4)\), using the rule \((x,y)\to(y, - x)\), we substitute \(x = 1\) and \(y=-4\). Then \(x'=-4\) and \(y'=-1\). So \(E'( - 4,-1)\)

Step3: Find coordinates of \(F(9,-4)\)

For point \(F(9,-4)\), substitute \(x = 9\) and \(y=-4\) into the rule \((x,y)\to(y, - x)\). Then \(x'=-4\) and \(y'=-9\). So \(F'(-4,-9)\)

Step4: Find coordinates of \(G(9,0)\)

For point \(G(9,0)\), substitute \(x = 9\) and \(y = 0\) into the rule \((x,y)\to(y, - x)\). Then \(x'=0\) and \(y'=-9\). So \(G'(0,-9)\)

Step5: Find coordinates of \(H(1,0)\)

For point \(H(1,0)\), substitute \(x = 1\) and \(y = 0\) into the rule \((x,y)\to(y, - x)\). Then \(x'=0\) and \(y'=-1\). So \(H'(0,-1)\)

Answer:

\(E'(-4,-1)\), \(F'(-4,-9)\), \(G'(0,-9)\), \(H'(0,-1)\)