Question

Triangle ABC has vertices at A(−5, 2), B(1, 3), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units right.

A′(−9, 2), B′(−3, 3), C′(−7, 0)
A′(−4, 6), B′(0, 7), C′(−5, 4)
A′(−1, 2), B′(5, 3), C′(1, 0)
A′(−5, −2), B′(1, −1), C′(−3, −4)

Answer 1

To find the coordinates of the vertices for triangle ABC after a translation of 4 units to the right, we start with the original coordinates of the vertices:

- A(−5, 2)
- B(1, 3)
- C(−3, 0)

When translating a point (x, y) to the right by d units, the new coordinates become (x + d, y). In this case, we will translate each vertex 4 units to the right.

1. For vertex A(−5, 2):
\[
A' = (−5 + 4, 2) = (−1, 2)
\]

2. For vertex B(1, 3):
\[
B' = (1 + 4, 3) = (5, 3)
\]

3. For vertex C(−3, 0):
\[
C' = (−3 + 4, 0) = (1, 0)
\]

Thus, the new coordinates after translation are:
- A′(−1, 2)
- B′(5, 3)
- C′(1, 0)

Therefore, the correct image coordinates after translation is:
**A′(−1, 2), B′(5, 3), C′(1, 0)** which corresponds to the third option.