Given point A (2,6) on the triangle, where would the new point on the triangle be after a rotation of 90 degrees counterclockwise
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).
To rotate a point counterclockwise by 90 degrees, we can use the following formula:
New_x = -y
New_y = x
Let's apply this formula to point A (2,6):
New_x = -6 = -6
New_y = 2
So, after a rotation of 90 degrees counterclockwise, the new point on the triangle would be (-6, 2).