To solve this problem of rotating the figure 90° counterclockwise about the origin, we use the following rule for rotation:

Rule for 90° Counterclockwise Rotation:

If a point $(x, y)$ is rotated 90° counterclockwise about the origin, its image becomes: $(x, y) \to (-y, x)$

Given Points:

1. $A(1, -1)$
2. $B(5, -6)$
3. $C(1, -6)$

We apply the rule $(x, y) \to (-y, x)$ to each point:

1. For $A(1, -1)$: $(x, y) = (1, -1) \to (-(-1), 1) = (1, 1)$ New coordinates: $A'(1, 1)$

2. For $B(5, -6)$: $(x, y) = (5, -6) \to (-(-6), 5) = (6, 5)$ New coordinates: $B'(6, 5)$

3. For $C(1, -6)$: $(x, y) = (1, -6) \to (-(-6), 1) = (6, 1)$ New coordinates: $C'(6, 1)$

Final Coordinates of the Image:

After rotating 90° counterclockwise, the new vertices are:

• $A'(1, 1)$
• $B'(6, 5)$
• $C'(6, 1)$

Let me know if you need further clarification or additional steps!

Follow-Up Questions:

1. What happens to the coordinates if the rotation is 90° clockwise?
2. How would you rotate these coordinates 180° about the origin?
3. Can you plot the original and rotated points on the graph?
4. What would be the effect of rotating the figure 270° counterclockwise?
5. How does this rule generalize to other rotations like 360°?

Tip:

For any rotation about the origin, always follow the standard coordinate rules for rotation to avoid errors.