To determine the point (6, 7) after a translation and a rotation, we'll follow the steps as outlined.
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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).
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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 \((-2, -2)\).
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