Question

Triangle ABC with vertices A(-2, -3), B(5, -1), and C(2, 2) is translated by (x,y) → (x - 1, y + 2). Then the image, triangle A'B'C', is translated by (x, y) + (x + 2, y - 1), resulting in A"B"C".​

Answer 1

• A"(-1, -2)
• B"(6, 0)
• C"(3, 3)
• (x, y) ⇒ (x+1, y+1)

Explanation:

Translation vectors add, and the addition is commutative and associative.

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The first translation adds (-1, 2) to the original coordinates. The second translation adds (2, -1) to the original coordinates. The two translations together add ...

(-1, 2) +(2, -1) = (-1+2, 2-1) = (1, 1)

to the original coordinates.

The single rule representing this translation is ...

(x, y) ⇒ (x +1, y +1)

Then the doubly-translated coordinates are ...

A(-2, -3) ⇒ A"(-1, -2)

B(5, -1) ⇒ B"(6, 0)

C(2, 2) ⇒ C"(3, 3)