A triangle has vertices (-3, 2), (0, 5), and (4, 2). What are the vertices after translating the triangle 3 units up? Draw a graph if necessary.

Answer 1

To translate the triangle 3 units up, we need to add 3 to the y-coordinate of each vertex.

The original vertices of the triangle are:

• \( A(-3, 2) \)
• \( B(0, 5) \)
• \( C(4, 2) \)

Now, we'll calculate the new coordinates after translating each vertex 3 units up:

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

2. For vertex \( B(0, 5) \): \[ B'(0, 5 + 3) = B'(0, 8) \]

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

So the new vertices after the translation are:

• \( A'(-3, 5) \)
• \( B'(0, 8) \)
• \( C'(4, 5) \)

Summary

The translated vertices of the triangle are:

• \( A'(-3, 5) \)
• \( B'(0, 8) \)
• \( C'(4, 5) \)

Graph

While I can't draw directly, here's how you can visualize it:

1. Plot the original vertices \( A(-3, 2) \), \( B(0, 5) \), and \( C(4, 2) \).
2. Then plot the new vertices \( A'(-3, 5) \), \( B'(0, 8) \), and \( C'(4, 5) \).
3. Draw the original triangle and the new triangle formed by the translated points.

This translation moves the triangle upwards, keeping the same x-coordinates but increasing all y-coordinates by 3.