Question

Triangle ABC is shown. Use the graph to answer the question.

triangle ABC on a coordinate plane with vertices at negative 8 comma 1, 0 comma 1, negative 4 comma 5

Determine the coordinates of the image if triangle ABC is translated 6 units to the right.

A′(−2, 1), B′(6, 1), C′(2, 5)
A′(−2, 1), B′(−6, 1), C′(−10, 5)
A′(−6, 7), B′(0, 7), C′(−4, 11)
A′(−6, −5), B′(0, −5), C′(−4, −1)

Answer 1

To translate triangle ABC, we need to add 6 units to the x-coordinate of each vertex.

The vertices of triangle ABC are:
- A(-8, 1)
- B(0, 1)
- C(-4, 5)

Let's translate each vertex:

1. For vertex A(-8, 1):
- New x-coordinate: -8 + 6 = -2
- New y-coordinate: 1 (remains the same)
- New coordinates for A' are (-2, 1).

2. For vertex B(0, 1):
- New x-coordinate: 0 + 6 = 6
- New y-coordinate: 1 (remains the same)
- New coordinates for B' are (6, 1).

3. For vertex C(-4, 5):
- New x-coordinate: -4 + 6 = 2
- New y-coordinate: 5 (remains the same)
- New coordinates for C' are (2, 5).

Now we can compile the new coordinates of triangle A'B'C':
- A'(-2, 1)
- B'(6, 1)
- C'(2, 5)

Thus, the image of triangle ABC after being translated 6 units to the right is A'(-2, 1), B'(6, 1), C'(2, 5).

The correct answer from the options is:
**A′(−2, 1), B′(6, 1), C′(2, 5)**.