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

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).