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'

Question

alexira [117]

2 years ago

13

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".

Mathematics

1 answer:

Elan Coil [88] · Answer 1 · 2023-09-22T02:46:14+03:00

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)