Question

parallelogram abcd is rotated to create image abcd. which rule describes the transformation? (x, y) → (y, -x) (x, y) → (-y, x) (x, y) → (-x, -y) (x, y) → (x, -y)

Explanation:

Step1: Find coordinates of points

Let's assume coordinates: \(A(2,5)\), \(B(5,4)\), \(C(5,2)\), \(D(2,3)\). After rotation, \(A'(5, - 2)\), \(B'(4,-5)\), \(C'(2,-5)\), \(D'(3,-2)\).

Step2: Check transformation rules

• For \((x,y)\to(y, - x)\): If \(A(2,5)\), then \((5,-2)\) (matches \(A'\)). If \(B(5,4)\), then \((4,-5)\) (matches \(B'\)). If \(C(5,2)\), then \((2,-5)\) (matches \(C'\)). If \(D(2,3)\), then \((3,-2)\) (matches \(D'\)).
• For \((x,y)\to(-y,x)\): If \(A(2,5)\), then \((-5,2)\) (does not match \(A'\)).
• For \((x,y)\to(-x,-y)\): If \(A(2,5)\), then \((-2,-5)\) (does not match \(A'\)).
• For \((x,y)\to(x,-y)\): If \(A(2,5)\), then \((2,-5)\) (does not match \(A'\)).

Answer:

\((x,y)\to(y, - x)\)