Question

Point G is rotated 90°. The coordinate of the pre-image point G was (7, –5), and its image G’ is at the coordinate (5, 7). What is the direction of the rotation?
counter-clockwise
horizontally
symmetrical
clockwise

Answer 1

To determine the direction of the rotation, we start with the coordinates of the pre-image point G, which is (7, -5).

When rotating a point 90° counter-clockwise, the formula for the new coordinates (x', y') in a 90° rotation is given by:

\[
(x', y') = (-y, x)
\]

Applying this to point G:

1. The x-coordinate of G is 7 and the y-coordinate is -5.
2. After applying the counter-clockwise rotation formula:

\[
x' = -(-5) = 5
\]
\[
y' = 7
\]

Thus, the image point G’ would be (5, 7), which matches the coordinates provided for G’.

Therefore, the direction of the rotation is **counter-clockwise**.