In the coordinate plane, which of the following functions rotates a point, (x, y), 90° counterclockwise about the point (1, 0)?

Question

In the coordinate plane, which of the following functions rotates a point, (x, y), 90° counterclockwise about the point (1, 0)?

A. T(x,y)=(1−y,x−1)

B. T(x,y)=(y+1,1−x)

C. T(x,y)=(x+1,y)

D. T(x,y)=(1−y,x)

Answer 1

To answer this question, let's first remind ourselves that rotation is a geometric transformation that involves rotating a figure, or a point in this case, about a fixed point called the center of rotation. Importantly, the distance between the figure, or point, being rotated and the center of rotation does not change throughout the rotation. We will use this idea to get our answer.

For simplicity, let's choose the point (2,0) to rotate 90° counterclockwise around the point (1,0). Before the rotation, our point is one unit to the right of (1,0). After rotating it 90° counterclockwise, it will be one unit above (1,0) at (1,1), with the distance between the two points still at one unit. This gives us the transformation (2,0) → (1,1). Function A fits this transformation:

T(x,y) = (1-y, x-1)

T (2,0) = (1-0, 2-1) = (1,1)