Question

What is the image of the point (8,4) after a rotation of 90° counterclockwise about the origin?​

Answer 1

Answer:  (-4, 8)

=========================================================

Explanation:

The 90 degree counterclockwise rotation rule we use is

$(x,y) \to (-y,x)$

the x and y coordinates swap places, and we change the sign of the first coordinate after the swap.

After using that rotation rule, we would go from (8,4) to (-4, 8) which is the final answer.

----------------

Extra info (optional section):

Define the following three points

A = (0,0)

B = (8,4)

C = (-4,8)

Use the slope formula to find that AB and AC have slopes of 1/2 and -2 in that order.

Those slopes multiply to -1, since (1/2)*(-2) = -1. This is a property of any two perpendicular lines as long as neither line is vertical and neither is horizontal. So this is sufficient to prove that the lines are perpendicular. This further means that a 90 degree rotation has taken place.