JEE Main Maths: Coordinate Geometry / Properties of Triangles questions with solutions

Q1. In triangle ABC, the medians AD and CF meet at the centroid G and are mutually perpendicular there. If BC = 3 cm and AB = 4 cm, find the length of AC (in cm).

1. sqrt(5)
2. sqrt(6)
3. 2
4. sqrt(7)

Answer: sqrt(5)

A standard result: if the medians from vertices A and C are perpendicular, then b² (the side AC) satisfies AB² + BC² = 5*AC². Substitute the given lengths.