Question

What is the result of rotating the given points 90° counter-clockwise around the origin and then reflecting them over the x-axis?

a) (0, 8) (5, 11) (10, 4) (4, 6)
b) (-8, 0) (-11, -5) (-4, -10) (-6, -4)
c) (8, 0) (11, 5) (4, 10) (6, 4)
d) (-8, 0) (11, 5) (4, 10) (-6, -4)

Answer 1

To rotate the given points 90° counter-clockwise around the origin and then reflect them over the x-axis, apply the rotation formula (x', y') = (-y, x) and then change the sign of the y-coordinate for each point.

Step-by-step explanation:

To rotate a point 90° counter-clockwise around the origin, we can use the formula:

(x', y') = (-y, x)

The given points are (0, 8), (5, 11), (10, 4), and (4, 6).

By applying the formula, we get the rotated points as follows:

(0, 8) -> (8, 0)
(5, 11) -> (-11, 5)
(10, 4) -> (-4, 10)
(4, 6) -> (-6, 4)

To reflect a point over the x-axis, we simply change the sign of the y-coordinate. Therefore, the final result after reflecting the rotated points over the x-axis is:

(8, 0), (-11, -5), (-4, -10), (-6, -4)