The transformation rule needed to generate the triangle E'F'G' is (x, y) → (x - 4, y + 11).
<h3>What is the transformation rule for the translation of a triangle?</h3>
Herein we see the triangle EFG and the triangle E'F'G', result of the translation of the former triangle.
A triangle is generated by three non-collinear points. Translation is a kind of rigid transformation and there is a translation if and only if each pair of related points is related to one and same translation vector:
T(x, y) = P'(x, y) - P(x, y) (1)
Where:
- P(x, y) - Original point
- P'(x, y) - Resulting point
Now we proceed to check if the triangle E'F'G' is the result of a translation:
T₁(x, y) = E'(x, y) - E(x, y)
T₁(x, y) = (- 9, 4) - (- 5, - 7)
T₁(x, y) = (- 4, 11)
T₂(x, y) = F'(x, y) - F(x, y)
T₂(x, y) = (- 7, 8) - (3, - 3)
T₂(x, y) = (- 4, 11)
T₃(x, y) = G'(x, y) - G(x, y)
T₃(x, y) = (- 2, 3) - (2, - 8)
T₃(x, y) = (- 4, 11)
The transformation rule needed to generate the triangle E'F'G' is (x, y) → (x - 4, y + 11).
To learn more on rigid transformations: brainly.com/question/28004150
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