https://file.aiquickdraw.com/mathbot/file/1725406270231am6hw239.jpg

https://file.aiquickdraw.com/mathbot/file/1725406270233bfakw4yu.jpg

To solve this problem, let's start by identifying the coordinates of the vertices of triangle \(ABC\) from the first image.

### Original Coordinates:
- \( A(4, 6) \)
- \( B(2, 1) \)
- \( C(6, 2) \)

### Translation of Triangle:
The problem asks us to translate the triangle \(ABC\) by 3 units to the left and 5 units down. A translation by \(a\) units to the left means subtracting \(a\) from the x-coordinates, and a translation by \(b\) units down means subtracting \(b\) from the y-coordinates.

### New Coordinates:
- \( A'(4 - 3, 6 - 5) = A'(1, 1) \)
- \( B'(2 - 3, 1 - 5) = B'(-1, -4) \)
- \( C'(6 - 3, 2 - 5) = C'(3, -3) \)

Now, let's match these calculated coordinates to the options provided in the second image:

### Correct Answer:
- The correct choice from the options is **\(A'(1, 1)\), \(B'(-1, -4)\), \(C'(3, -3)\)**.

If you have any questions or need further details, feel free to ask!

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Here are five related questions to expand on this topic:

1. How would the translation change if the triangle was moved 4 units to the right and 2 units up?
2. What is the effect of a reflection over the x-axis on the coordinates of a triangle?
3. How can you determine the area of the translated triangle \(A'B'C'\)?
4. What would be the new coordinates if the triangle \(ABC\) was rotated 90 degrees counterclockwise about the origin?
5. How do you find the midpoint of the segment joining \(B'\) and \(C'\)?

**Tip:** When translating geometric figures, always adjust both x and y coordinates by the specified amounts to ensure accurate transformations.

Translate triangle ABC by 3 units to the left and 5 units down. Which of the following are the coordinates of the new triangle A'B'C'?

Learn how to translate triangle ABC by 3 units to the left and 5 units down on the coordinate plane. Understand the steps to calculate the new coordinates of the vertices A', B', and C'. Suitable for students in Grades 6-8.

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