Question

What is point
(6, 7) after a translation of
4 units left and 5 units down followed by a 180° clockwise rotation around the origin.

Answer 1

To determine the point (6, 7) after a translation and a rotation, we'll follow the steps as outlined.

1. **Translation**:
- Move 4 units left means subtracting 4 from the x-coordinate.
- Move 5 units down means subtracting 5 from the y-coordinate.

Starting with (6, 7):
- New x-coordinate: \( 6 - 4 = 2 \)
- New y-coordinate: \( 7 - 5 = 2 \)

After translation, the point becomes (2, 2).

2. **180° Clockwise Rotation around the origin**:
- A 180° rotation clockwise can be achieved through the transformation rule: \( (x, y) \to (-x, -y) \).

Applying this transformation to (2, 2):
- New x-coordinate: \( -2 \)
- New y-coordinate: \( -2 \)

After the rotation, the point becomes (-2, -2).

So, after a translation of 4 units left and 5 units down followed by a 180° clockwise rotation around the origin, the final point is \((-2, -2)\).