https://file.aiquickdraw.com/mathbot/file/1729461334672729m8vtq.jpg

Let's solve the problem step by step:

### Points Given:
- \( A(-2, 1) \)
- \( B(-3, 4) \)
- \( C(2, -5) \)

### Step 1: Translate 5 units left and 3 units up
Translation rule:  
- Subtract 5 from the \( x \)-coordinate (5 units left).
- Add 3 to the \( y \)-coordinate (3 units up).

#### New coordinates after translation:
- For \( A \): \( (-2 - 5, 1 + 3) = (-7, 4) \)
- For \( B \): \( (-3 - 5, 4 + 3) = (-8, 7) \)
- For \( C \): \( (2 - 5, -5 + 3) = (-3, -2) \)

So after translation:
- \( A'(-7, 4) \)
- \( B'(-8, 7) \)
- \( C'(-3, -2) \)

### Step 2: Rotate 90° counterclockwise about the origin
Rotation rule for 90° counterclockwise:  
- New \( x' = -y \)
- New \( y' = x \)

#### New coordinates after rotation:
- For \( A'(-7, 4) \):  
  \( A''(-4, -7) \) (since \( x' = -4 \), \( y' = -7 \))
  
- For \( B'(-8, 7) \):  
  \( B''(-7, -8) \)
  
- For \( C'(-3, -2) \):  
  \( C''(2, -3) \)

### Final Answer:
- \( A''(-4, -7) \)
- \( B''(-7, -8) \)
- \( C''(2, -3) \)

Would you like more details on any of these steps? 

Here are 5 related questions to explore further:
1. How do you perform a 180° rotation instead of 90°?
2. What is the rule for rotating 90° clockwise?
3. Can you describe how a dilation transformation would affect these points?
4. How would a reflection over the x-axis change the final coordinates?
5. What if the translation was 5 units right instead of left?

**Tip:** When rotating points around the origin, always check the direction (clockwise or counterclockwise) carefully to apply the correct transformation rule.

Translate points A(-2, 1), B(-3, 4), C(2, -5) 5 units left and 3 units up, and rotate 90° counterclockwise about the origin. What are the new coordinates?

Learn how to translate points 5 units left and 3 units up, then rotate them 90° counterclockwise about the origin. Example: Points A(-2, 1), B(-3, 4), and C(2, -5) are transformed step-by-step. Suitable for Grades 8-10.

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