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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".​

Triangle ABC With Vertices A2 3 B5 1 And C2 2 Is Translated By Xy X 1 Y 2 Then The Image Triangle ABC Is Translated By X Y X 2 Y 1 Resulting In ABC class=

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Sqdancefanidn

Answer:

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

Step-by-step 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)

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