Given a point (-7, 4)on a geometric figure, what is a new point after rotating the figure 90 degrees counterclockwise?
To find a new point after rotating a figure 90 degrees counterclockwise, we need to swap the x and y coordinates of the given point and negate the new x coordinate.
So, if the given point is (-7, 4), after rotating it 90 degrees counterclockwise, the new point would be (4, 7).
To find the new point after rotating the figure 90 degrees counterclockwise, we need to use the rotation formula.
The rotation formula is as follows:
(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)
Given:
Initial point = (-7, 4)
Rotation angle = 90 degrees counterclockwise
Now, we substitute the values into the formula:
x' = -7 * cos(90) - 4 * sin(90)
= -7 * 0 - 4 * 1
= 0
y' = -7 * sin(90) + 4 * cos(90)
= -7 * 1 + 4 * 0
= -7
Therefore, the new point after rotating the figure 90 degrees counterclockwise is (0, -7).