Question

Given point A (2,6) on the triangle, where would the new point on the triangle be after a rotation of 90 degrees counterclockwise

Answer 1

To find the new coordinates of a point after a rotation of 90 degrees counterclockwise, we can use the rotation formula:

x' = cos(θ) * x - sin(θ) * y
y' = sin(θ) * x + cos(θ) * y

In this case, we want to rotate point A (2,6) by 90 degrees counterclockwise.

θ = 90 degrees

Plugging the values into the rotation formula, we get:

x' = cos(90) * 2 - sin(90) * 6
y' = sin(90) * 2 + cos(90) * 6

Since cos(90) = 0 and sin(90) = 1, the equations simplify to:

x' = 0 * 2 - 1 * 6 = -6
y' = 1 * 2 + 0 * 6 = 2

Therefore, the new point after rotating A (2,6) by 90 degrees counterclockwise is (-6, 2).