Question: Triangle MNO has vertices M(-3, -6), N(-8,-4), and O(-6,-2). What would the coordinates be after a 90 degree counterclockwise rotation?
M'(type your answer..., type your answer...)
N'(type your answer..., type your answer...)
O'(type your answer..., type your answer...)
1. **State the problem:** We have triangle MNO with vertices \(M(-3, -6)\), \(N(-8, -4)\), and \(O(-6, -2)\). We want to find the coordinates of these points after a 90 degree counterclockwise rotation about the origin.
2. **Formula for 90° counterclockwise rotation:**
For any point \((x, y)\), the coordinates after a 90° counterclockwise rotation about the origin are given by:
$$ (x', y') = (-y, x) $$
This means we swap the coordinates and change the sign of the original \(y\) coordinate.
3. **Apply the formula to each vertex:**
- For \(M(-3, -6)\):
$$ x' = -(-6) = 6 $$
$$ y' = -3 $$
So, \(M' = (6, -3)\).
- For \(N(-8, -4)\):
$$ x' = -(-4) = 4 $$
$$ y' = -8 $$
So, \(N' = (4, -8)\).
- For \(O(-6, -2)\):
$$ x' = -(-2) = 2 $$
$$ y' = -6 $$
So, \(O' = (2, -6)\).
4. **Final answer:**
The coordinates after a 90 degree counterclockwise rotation are:
\[ M'(6, -3), \quad N'(4, -8), \quad O'(2, -6) \]
This completes the problem.