Answer:
- P''(2, 1)
- N''(1, -2)
- B''(5, -3)
Explanation:
You want the image coordinates for P(2, 2), N(3, -1), and B(-1, -2) after translation by (x, y) ⇒ (x, y-1) and reflection over x = 2.
Reflection
Reflection over x=2 is the transformation ...
(x, y) ⇒ (4 -x, y)
Glide Reflection
When the reflection occurs after the given translation, the composite transformation is ...
(x, y) ⇒ (4 -x, y -1)
Then the image points are ...
P(2, 2) ⇒ P''(4 -2, 2 -1) = P''(2, 1)
N(3, -1) ⇒ N''(4 -3, -1 -1) = N''(1, -2)
B(-1, -2) ⇒ B''(4 -(-1), -2 -1) = B''(5, -3)
The transformed coordinates are ...
- P''(2, 1)
- N''(1, -2)
- B''(5, -3)
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Additional comment
Reflection over x=a has the transformation (x, y) ⇒ (2a -x, y). Similarly, the reflection over y=a has the transformation (x, y) ⇒ (x, 2a -y).
Note that point P lies on the line of reflection, so its x-coordinate is unchanged.
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