Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.

Question

A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)

Answer 1

To translate a point \( (x, y) \) 3 units up, you add 3 to the y-coordinate.

Let's find the new coordinates for each vertex after translating them 3 units up:

1. For point A(-3, 3): \[ A'(-3, 3+3) = A'(-3, 6) \]

2. For point B(0, 7): \[ B'(0, 7+3) = B'(0, 10) \]

3. For point C(-3, 0): \[ C'(-3, 0+3) = C'(-3, 3) \]

So the coordinates of the new vertices after the translation are: \( A'(-3, 6) \), \( B'(0, 10) \), \( C'(-3, 3) \).

This matches the second option in your list:

A′(−3, 6), B′(0, 10), C′(−3, 3).