What are the coordinates of the other vertices of the translated triangle?

The original triangle has vertices at:

• Point A: $(1,6)$
• Bottom-left vertex: $(1,3)$
• Bottom-right vertex: $(2,3)$ Point A is translated to point B, which is at $(5,4)$.

To find the translation, we calculate the change in the x-coordinate and the change in the y-coordinate from A to B.

• Change in x-coordinate: $5 - 1 = 4$ (4 units to the right)
• Change in y-coordinate: $4 - 6 = -2$ (2 units down) So, the translation is 4 units right and 2 units down.

• For the original bottom-left vertex $(1,3)$:
  • New x-coordinate: $1 + 4 = 5$
  • New y-coordinate: $3 - 2 = 1$
  • Translated vertex: $(5,1)$
• For the original bottom-right vertex $(2,3)$:
  • New x-coordinate: $2 + 4 = 6$
  • New y-coordinate: $3 - 2 = 1$
  • Translated vertex: $(6,1)$

The coordinates of the other vertices of the translated triangle are $\boxed{(5,1) \text{ and } (6,1)}$.

How did you work this out?
I worked this out by first determining the translation that moved point A to point B. I found that the x-coordinate increased by 4 and the y-coordinate decreased by 2. Then, I identified the coordinates of the other two vertices of the original triangle. Finally, I applied the same translation (adding 4 to the x-coordinate and subtracting 2 from the y-coordinate) to each of these two vertices to find their new positions in the translated triangle.