Question

Find H' after the indicated rotation.
Triangle FGH with vertices F(-7,8), G(-1, 1),

Answer 1

To find H' after the indicated rotation, determine the coordinates of the new point using the rotation formula.

Step-by-step explanation:

To find H' after the indicated rotation, we need to determine the coordinates of the new point after the rotation. Let's first find the center of rotation, which is the midpoint of FG. The x-coordinate of the center is given by (x1 + x2) / 2, and the y-coordinate is given by (y1 + y2) / 2. In this case, the center is ((-7 + (-1)) / 2, (8 + 1) / 2), which is (-4, 4.5).

We can now use the formula for rotating a point (x, y) counterclockwise by an angle θ about the origin:

x' = x*cos(θ) - y*sin(θ)

y' = x*sin(θ) + y*cos(θ)

Substituting the values, we have:

x' = (-7)*cos(θ) - 8*sin(θ)

y' = (-7)*sin(θ) + 8*cos(θ)