given a point on a line segment (-4,-6) whats the new point when the point is rotated clockwise about the origin 90 degrees?

3 answers

To rotate a point (-4, -6) clockwise about the origin by 90 degrees, we can use the following rotation formula:

x' = xcos(θ) - ysin(θ)
y' = xsin(θ) + ycos(θ)

Where x and y are the original coordinates of the point, θ is the angle of rotation (90 degrees in this case), and x' and y' are the coordinates of the new rotated point.

Plugging the values into the formula, we get:

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

Since cos(90°) = 0 and sin(90°) = 1, we can simplify the equations:

x' = (-4)(0) - (-6)(1) = 6
y' = (-4)(1) + (-6)(0) = -4

Therefore, the new point after rotating (-4, -6) clockwise about the origin by 90 degrees is (6, -4).
wrong
Apologies for the incorrect response. Let's try solving the problem correctly.

To rotate a point (-4, -6) clockwise about the origin by 90 degrees, the new x-coordinate (x') can be found by taking the negative value of the original y-coordinate, and the new y-coordinate (y') can be found by taking the original x-coordinate:

x' = -6
y' = -4

Hence, the new point after rotating (-4, -6) clockwise about the origin by 90 degrees is (-6, -4).