Question

Find the coordinates of the vertices of the point U after the given transformation (rotation 90° counterclockwise about the origin) if U(-5, 4).

a) (4, 5)
b) (-5, -4)
c) (-4, 5)
d) (5, -4)

Answer 1

To find the coordinates of the point U after a counterclockwise rotation of 90° about the origin, substitute the values into the rotation formula and simplify the expressions.

Step-by-step explanation:

To find the coordinates of the vertices of the point U after a counterclockwise rotation of 90° about the origin, we can use the rotation formula:

x' = x*cos(θ) - y*sin(θ)

y' = x*sin(θ) + y*cos(θ)

Given that U(-5, 4), substituting the values into the formula, we get:

x' = -5*cos(90°) - 4*sin(90°)

y' = -5*sin(90°) + 4*cos(90°)

Simplifying the expressions, we get:

x' = 4

y' = -5

Therefore, the coordinates of the point U after the rotation are (4, -5).