Question

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

triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2

Determine the coordinates of the image if triangle ABC is translated 4 units down.
A′(1, −6), B′(9, −6), C′(5, −2)
A′(1, 2), B′(9, 2), C′(5, 6)
A′(5, −2), B′(13, −2), C′(9, 2)
A′(−3, −2), B′(5, −2), C′(1, 2)

Answer 1

To determine the coordinates of the image of triangle ABC after being translated 4 units down, we need to subtract 4 from the y-coordinate of each vertex of the triangle.

The original coordinates of the vertices are:
- A(1, -2)
- B(9, -2)
- C(5, 2)

Now, let's translate each vertex down 4 units:

1. For point A:
\[
A'(1, -2 - 4) = A'(1, -6)
\]

2. For point B:
\[
B'(9, -2 - 4) = B'(9, -6)
\]

3. For point C:
\[
C'(5, 2 - 4) = C'(5, -2)
\]

After the translation, the new coordinates are:
- A′(1, -6)
- B′(9, -6)
- C′(5, -2)

Thus, the coordinates of the image after the translation are:
**A′(1, −6), B′(9, −6), C′(5, −2)**

So the correct answer is:
**A′(1, −6), B′(9, −6), C′(5, −2)**.