To translate triangle ABC to a new position on the coordinate plane, we apply the translation rule (x, y) -> (x + 4, y + 6) to each vertex of the triangle.
The vertices of triangle ABC are given as follows:
- Point A(1, 5)
- Point B(-1, 2)
- Point C(3, 1)
Now, let’s apply the translation rule to each point:
- For point A(1, 5):
- New A = (1 + 4, 5 + 6) = (5, 11)
- For point B(-1, 2):
- New B = (-1 + 4, 2 + 6) = (3, 8)
- For point C(3, 1):
- New C = (3 + 4, 1 + 6) = (7, 7)
After translating all the points, the new coordinates of triangle ABC are:
- A'(5, 11)
- B'(3, 8)
- C'(7, 7)
This means that triangle ABC has been moved 4 units to the right and 6 units up on the coordinate plane.