The image after the composition is X''(9, -1), Y'(13, -5), and Z''(14, -3)
How to determine the image after the composition?
The vertices of the triangle are given as:
X(2, 4), Y(6, 0), and Z(7, 2)
The compositions of translations are given as:
Translation: (x, y) → (x + 12, y + 4)
Translation: (x, y) → (x − 5, y − 9)
So, we have:
Translation: (x, y) → (x + 12, y + 4)
X'(2 + 12, 4 +4), Y'(6 + 12, 0 + 4), and Z'(7 + 12, 2 + 4)
Evaluate
X'(14, 8), Y'(18, 4), and Z'(19, 6)
Translation: (x, y) → (x − 5, y − 9)
X''(14 - 5, 8 - 9), Y'(18 - 5, 4 - 9), and Z'(19 - 5, 6 - 9)
Evaluate
X''(9, -1), Y'(13, -5), and Z''(14, -3)
Hence, the image after the composition is X''(9, -1), Y'(13, -5), and Z''(14, -3)
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