What is the new point when you rotate a geometric figure with point (5, 8) 270 degrees counterclockwise about the origin?
To rotate a point counterclockwise about the origin, we can use the following rotation formulas:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
In this case, the given point is (5, 8) and we want to rotate it 270 degrees counterclockwise. Let's substitute these values into the formulas:
x' = 5 * cos(270°) - 8 * sin(270°)
y' = 5 * sin(270°) + 8 * cos(270°)
However, we can simplify these formulas as follows:
x' = -8 * sin(270°)
y' = 5 * cos(270°)
Now, let's calculate the values:
x' = -8 * (-1) = 8
y' = 5 * 0 = 0
Therefore, when we rotate the point (5, 8) 270 degrees counterclockwise about the origin, the new point is (8, 0).
To rotate a point counterclockwise about the origin, you can use the following rotation formula:
x' = x * cos(angle) - y * sin(angle)
y' = x * sin(angle) + y * cos(angle)
In this case, the original point (5, 8) needs to be rotated 270 degrees counterclockwise.
Plugging the values into the formula:
x' = 5 * cos(270) - 8 * sin(270)
y' = 5 * sin(270) + 8 * cos(270)
Since cos(270) = 0 and sin(270) = -1, we can simplify the formula:
x' = 5 * 0 - 8 * (-1) = 8
y' = 5 * (-1) + 8 * 0 = -5
Therefore, the new point after rotating (5, 8) 270 degrees counterclockwise about the origin is (8, -5).