Question

Point M (0,4) is rotated about the origin 270 degrees. What are the coordinates of M′




(1 point)
(
,
)

Answer 1

To rotate the point \( M(0, 4) \) about the origin by 270 degrees, we can use the rotation formula. A rotation of \( \theta \) degrees around the origin transforms a point \( (x, y) \) to \( (x', y') \) using the following formulas:

\[
x' = x \cos(\theta) - y \sin(\theta)
\]
\[
y' = x \sin(\theta) + y \cos(\theta)
\]

For a rotation of 270 degrees, we can substitute \( \theta = 270^\circ \):

- \( \cos(270^\circ) = 0 \)
- \( \sin(270^\circ) = -1 \)

Now, we apply the formulas to the point \( (0, 4) \):

\[
x' = 0 \cdot 0 - 4 \cdot (-1) = 4
\]
\[
y' = 0 \cdot (-1) + 4 \cdot 0 = 0
\]

Thus, the coordinates of \( M' \) after the rotation are:

\[
M' (4, 0)
\]

So, the final answer is:

\[
(4, 0)
\]