Question

19
quadrilateral abcd has coordinates a (6, -6), b (3, -8), c (2, -6) and d (3, -4). determine the coordinates of the vertices of a b c d after a rotation of 90 degrees counterclockwise about (-2, -1). * (10 points)
a (2, 0), b (4, 3), c (2, 4) and d (0, 3)
a (-2, 0), b (-4, 3), c (-2, 4) and d (0, 3)
a (2, 0), b (4, -3), c (2, -4) and d (0, -3)
a (3, 7), b (5, 4), c (3, 3) and d (1, 4)

Explanation:

Step1: Translate the points

Subtract the center of rotation \((-2,-1)\) from each vertex.
For point \(A(6,-6)\): \((6 - (-2),-6-(-1))=(8,-5)\)
For point \(B(3,-8)\): \((3 - (-2),-8-(-1))=(5,-7)\)
For point \(C(2,-6)\): \((2 - (-2),-6-(-1))=(4,-5)\)
For point \(D(3,-4)\): \((3 - (-2),-4-(-1))=(5,-3)\)

Step2: Rotate the translated points 90° counter - clockwise

The rule for a 90° counter - clockwise rotation of a point \((x,y)\) is \((-y,x)\)
For translated point \((8,-5)\): \((5,8)\)
For translated point \((5,-7)\): \((7,5)\)
For translated point \((4,-5)\): \((5,4)\)
For translated point \((5,-3)\): \((3,5)\)

Step3: Translate the rotated points back

Add the center of rotation \((-2,-1)\) to each rotated point.
For \((5,8)\): \((5+(-2),8+(-1))=(3,7)\)
For \((7,5)\): \((7+(-2),5+(-1))=(5,4)\)
For \((5,4)\): \((5+(-2),4+(-1))=(3,3)\)
For \((3,5)\): \((3+(-2),5+(-1))=(1,4)\)

Answer:

A \((3,7)\), B \((5,4)\), C \((3,3)\) and D \((1,4)\)