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You are given the coordinates of a triangle and coordinates for only one of the vertices of its image under a translation. Explain how to translate the entire triangle.
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GPT-5 mini
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A translation moves every point by the same vector. So:
1. Identify which original vertex corresponds to the given image vertex (say original A(x,y) and its image A'(x',y')).
2. Compute the translation vector v = A' − A = (x' − x, y' − y).
3. Apply that vector to the other vertices: if B(x2,y2) and C(x3,y3) are the other vertices, then B' = B + v = (x2 + (x'−x), y2 + (y'−y)) and C' = C + v = (x3 + (x'−x), y3 + (y'−y)).
Example: A(1,2), B(4,3), C(2,5) and A'(3,6). Then v = (3−1, 6−2) = (2,4). So B' = (4+2, 3+4) = (6,7) and C' = (2+2, 5+4) = (4,9).
Note: if you don’t know which original vertex corresponds to the given image point, you cannot determine a unique translation.
1. Identify which original vertex corresponds to the given image vertex (say original A(x,y) and its image A'(x',y')).
2. Compute the translation vector v = A' − A = (x' − x, y' − y).
3. Apply that vector to the other vertices: if B(x2,y2) and C(x3,y3) are the other vertices, then B' = B + v = (x2 + (x'−x), y2 + (y'−y)) and C' = C + v = (x3 + (x'−x), y3 + (y'−y)).
Example: A(1,2), B(4,3), C(2,5) and A'(3,6). Then v = (3−1, 6−2) = (2,4). So B' = (4+2, 3+4) = (6,7) and C' = (2+2, 5+4) = (4,9).
Note: if you don’t know which original vertex corresponds to the given image point, you cannot determine a unique translation.
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