Question

A quadrilateral with vertices G(−10,1) , E(−6,−4) , O(2,0) , and M(0,4) is rotated about the origin 270 degrees (counterclockwise). Apply rotation mapping rules to find the image of M .

m'(answer here)

Answer 1

To find the image of point M(0, 4) after a 270-degree counterclockwise rotation about the origin, you can use the following rotation rules:

When rotating a point (x, y) about the origin through an angle θ, the new coordinates (x', y') can be found using the formulas:
- \( x' = x \cdot \cos(\theta) - y \cdot \sin(\theta) \)
- \( y' = x \cdot \sin(\theta) + y \cdot \cos(\theta) \)

For a 270-degree rotation, we can use the following values:
- \( \cos(270^\circ) = 0 \)
- \( \sin(270^\circ) = -1 \)

Now, applying the rotation to point M(0, 4):
- \( x = 0 \)
- \( y = 4 \)

Now substituting into the rotation formulas:
- \( x' = 0 \cdot 0 - 4 \cdot (-1) = 0 + 4 = 4 \)
- \( y' = 0 \cdot (-1) + 4 \cdot 0 = 0 + 0 = 0 \)

So the coordinates after the rotation are (4, 0).

Thus, the image of M after a 270-degree rotation about the origin is:

**M' = (4, 0)**