Question

1. 90° counterclockwise rotation

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original points

Assume the original points of the trapezoid are \(A(2,5)\), \(B(2, - 1)\), \(C(4,0)\), \(D(4,4)\).

Step3: Apply rotation rule to point A

For point \(A(2,5)\), using the rule \((x,y)\to(-y,x)\), we get \(A'(-5,2)\).

Step4: Apply rotation rule to point B

For point \(B(2,-1)\), \((x,y)\to(-y,x)\) gives \(B'(1,2)\).

Step5: Apply rotation rule to point C

For point \(C(4,0)\), \((x,y)\to(-y,x)\) gives \(C'(0,4)\).

Step6: Apply rotation rule to point D

For point \(D(4,4)\), \((x,y)\to(-y,x)\) gives \(D'(-4,4)\).

Answer:

\(A'(-5,2)\), \(B'(1,2)\), \(C'(0,4)\), \(D'(-4,4)\)