Question

A point P(3,4)is reflected in the x-axis, then rotated by 90 degrees clockwise about the origin.What are the coordinates of the image of P?

Answer 1

(-4, -3)

Explanation:

When a point is reflected in the x-axis, the x-coordinate does not change, and the y-coordinate becomes negative:

• (x, y) → (x, -y)

Therefore, if point P(3, 4) is reflected in the x-axis, then:

• P' = (3, -4)

When a point is rotated 90° clockwise about the origin, it produces a point that has the coordinates (y, -x):

• (x, y) → (y, -x)

Therefore, if point P'(3, -4) is rotated 90° clockwise about the origin, then:

• P'' = (-4, -3)