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.