To rotate a figure $\triangle MN$ around the origin $O$ by $90^\circ$, we apply the following transformation rules for a $90^\circ$ counterclockwise rotation about the origin:

$(x, y) \rightarrow (-y, x)$

Given:

• $M(3, -5)$
• $N(2, 4)$

Applying the transformation to each point:

1. For $M(3, -5)$: $M' = (-(-5), 3) = (5, 3)$

2. For $N(2, 4)$: $N' = (-4, 2)$

Final Coordinates After Rotation

• $M' = (5, 3)$
• $N' = (-4, 2)$

Thus, the rotated image $\triangle M'N'$ has vertices:

• $M'(5, 3)$
• $N'(-4, 2)$

Would you like more details or have any questions?

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Related Questions:

1. How does rotation work in three-dimensional space?
2. What are other common rotation angles and their transformation rules?
3. How do you find the center of rotation if it’s not the origin?
4. How does a 90° clockwise rotation differ in transformation rules?
5. What happens if the points are rotated by 180°?

Tip: When rotating points, always keep track of the direction (clockwise or counterclockwise), as it affects the transformation rules.