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 of \(A=(2,5)\), \(B=(5,4)\), \(D=(1,3)\). After rotation, \(A'=(5, - 2)\), \(B'=(4,-5)\), \(D'=(3,-1)\).

Step2: Check transformation rule

For point \(A=(x = 2,y = 5)\) and \(A'=(y=-2,x = 5)\) (incorrect).
For point \(A=(x = 2,y = 5)\) and \(A'=( - y=-5,x = 2)\) (incorrect).
For point \(A=(x = 2,y = 5)\), if \((x,y)\to(-x,-y)\), then \(A'=(-2,-5)\) (incorrect).
For point \(A=(x = 2,y = 5)\), if \((x,y)\to(y,-x)\), then \(A'=(5,-2)\).
For point \(B=(x = 5,y = 4)\), if \((x,y)\to(y,-x)\), then \(B'=(4,-5)\).
For point \(D=(x = 1,y = 3)\), if \((x,y)\to(y,-x)\), then \(D'=(3,-1)\).

Answer:

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