90 and 270 degree rotations quick check

Question

What is the new point when you rotate a geometric figure with point (5,8) 270 degrees counterclockwise about the origin

Answer 1

To rotate the point (5,8) 270 degrees counterclockwise about the origin, you can use the following approach:

Rotating a point (x, y) counterclockwise by 270 degrees is equivalent to rotating it by -90 degrees (which is the same as a clockwise rotation of 90 degrees). The general rule for a 90-degree clockwise rotation is:

\[ (x, y) \rightarrow (y, -x) \]

Applying this rule to the point (5, 8):

\[ (5, 8) \rightarrow (8, -5) \]

Therefore, the new point after rotating (5, 8) 270 degrees counterclockwise about the origin is \((8, -5)\).