Question

The vertices of a triangle are located at (3,-2), (3, -5), and (5, -3). The triangle is translated 5 units to the left and rotated 180 degrees about the origin. What are the coordinates of its image?

Answer 1

To translate a point to the left, subtract the desired amount from the x-coordinate and to rotate a point 180 degrees about the origin, change the signs of both the x and y coordinates.

Step-by-step explanation:

To translate a point to the left, we subtract the desired amount from the x-coordinate. To rotate a point 180 degrees about the origin, we change the signs of both the x and y coordinates. Applying these transformations to the given coordinates:

1. Translate 5 units to the left: (3, -2) -> (3 - 5, -2) -> (-2, -2)
2. Rotate 180 degrees about the origin: (-2, -2) -> (-(-2), -(-2)) -> (2, 2)

Therefore, the coordinates of the image triangle are (2, 2).