Question

which shows the image of rectangle abcd after the rotation $(x,y)\to(-y,x)?$

Explanation:

Answer:

Let's assume the coordinates of rectangle \(ABCD\) are \(A(- 3,0)\), \(B(-1,0)\), \(C(-1,3)\), \(D(-3,3)\)

Step1: Apply the rotation rule \((x,y)\to(-y,x)\) to each vertex

• For \(A(-3,0)\):

Substitute \(x = - 3\) and \(y = 0\) into \((x,y)\to(-y,x)\), we get \(A'(0,-3)\)

• For \(B(-1,0)\):

Substitute \(x=-1\) and \(y = 0\) into \((x,y)\to(-y,x)\), we get \(B'(0,-1)\)

• For \(C(-1,3)\):

Substitute \(x=-1\) and \(y = 3\) into \((x,y)\to(-y,x)\), we get \(C'(-3,-1)\)

• For \(D(-3,3)\):

Substitute \(x=-3\) and \(y = 3\) into \((x,y)\to(-y,x)\), we get \(D'(-3,-3)\)

Step2: Analyze the position of the new rectangle \(A'B'C'D'\)

The new rectangle \(A'B'C'D'\) has vertices \(A'(0,-3)\), \(B'(0,-1)\), \(C'(-3,-1)\), \(D'(-3,-3)\) which corresponds to the third - option (assuming the options are ordered from left - to - right as in the problem statement)