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Reflect object about y=x+1

Short answer

Reflection about y = x + 1 yields x' = y − 1, y' = x + 1. Point (2,3) lies on line, remains (2,3). (4,3) becomes (2,5); (4,5) remains (4,5). Reflected points: (2,3), (2,5), (4,5).

Reflect the object (2, 3), (4, 3), (4, 5) about the line y = x + 1.

The line y = x + 1 has m = 1 and c = 1.

M = T(0,1) · R(45°) · Ref_x · R(−45°) · T(0,−1)

              | 1−m²   2m   −2mc |   | 0 1 −1 |
 M = 1/(1+m²) | 2m   m²−1    2c  | = | 1 0  1 |
              |  0     0   1+m²  |   | 0 0  1 |

So x' = y − 1, y' = x + 1.

(2,3):  x' = 3 − 1 = 2,  y' = 2 + 1 = 3      -> (2,3)   (lies on the line)
(4,3):  x' = 3 − 1 = 2,  y' = 4 + 1 = 5      -> (2,5)
(4,5):  x' = 5 − 1 = 4,  y' = 4 + 1 = 5      -> (4,5)   (lies on the line)

Answer: the reflected points are (2,3), (2,5), (4,5).

✓ Answer checked by Claude Opus 5.5 (high effort)

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