144k views
3 votes
What is the image of the point (−4,−6) after a rotation of 90∘ counterclockwise about the origin?

User Mhansen
by
4.2k points

1 Answer

3 votes

Final answer:

The image of the point (-4,-6) after a rotation of 90° counterclockwise about the origin is (6,-4).

Step-by-step explanation:

To find the image of the point (-4,-6) after a rotation of 90° counterclockwise about the origin, we can apply the rotation formula.

The formula for rotating a point (x,y) counterclockwise about the origin by an angle θ is:

x' = x * cos(θ) - y * sin(θ)

y' = x * sin(θ) + y * cos(θ)

Using this formula, we can substitute the values x = -4, y = -6, and θ = 90° to find the new coordinates of the point after the rotation:

x' = -4 * cos(90°) - (-6) * sin(90°) = 6

y' = -4 * sin(90°) + (-6) * cos(90°) = -4

Therefore, the image of the point (-4,-6) after a rotation of 90° counterclockwise about the origin is (6,-4).

User Remdezx
by
3.0k points