Question

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.