To find the new coordinates of triangle A′B′C′ after translating triangle ABC by 3 units to the left and 5 units down, we need to apply these transformations to the original coordinates of points A, B, and C.
- Translation left by 3 units: This means we subtract 3 from the x-coordinate of each point.
- Translation down by 5 units: This means we subtract 5 from the y-coordinate of each point.
Let's say the original coordinates of A are (x_A, y_A), B are (x_B, y_B), and C are (x_C, y_C). After the transformations, the new coordinates A′, B′, and C′ will be:
- A′(x_A - 3, y_A - 5)
- B′(x_B - 3, y_B - 5)
- C′(x_C - 3, y_C - 5)
Now, we can evaluate which set of coordinates matches after performing the translation:
- If A is at (x_A, y_A), then the new coordinate A′ will be calculated as (x_A - 3, y_A - 5).
- Repeat this for points B and C.
Given the options, you would need the exact coordinates of the original triangle A, B, and C to find A′, B′, and C′ after the transformation.
Since the original coordinates are not provided, I cannot determine the selected answer without that information. However, once you calculate A′, B′, and C′ using the above transformation on the coordinates of triangle ABC, you can compare the results with the options provided to select the correct one. Please provide the original coordinates of triangle ABC to derive the translated coordinates.