Question

What are the coordinates of point E if E (-9, -3) is rotated 270 degrees clockwise around around the origin.

Answer 1

To find the coordinates of point E after a 270-degree clockwise rotation around the origin, we can use the formula for a 2D rotation.

The formula is:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)

In this case, the initial coordinates of point E are (-9, -3) and we want to rotate it 270 degrees clockwise, which is equivalent to rotating it 90 degrees counter-clockwise.

Let's plug in the values into the formulas:
x' = -9 * cos(90) - (-3) * sin(90)
y' = -9 * sin(90) + (-3) * cos(90)

Now, we need to use the trigonometric values of 90 degrees:
cos(90) = 0
sin(90) = 1

Substituting these values, we get:
x' = -9 * 0 - (-3) * 1 = 0 - (-3) = 3
y' = -9 * 1 + (-3) * 0 = -9 + 0 = -9

Therefore, after a 270-degree clockwise rotation around the origin, the coordinates of point E become (3, -9).