The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side​ (see the​ figure).

Question

Find the lengths of the medians of the triangle with vertices at

A=​(1​,1​),

B=​(9​,1​),

and

C=​(5​,9​).

Answer 1

A=​(1​,1​),

B=​(9​,1)

C=​(5​,9​)

Midpoint of AB M₁(5,1). So, CM₁ = √(5 - 5)² + (9 - 1)² = 8

Midpoint of AC M₂(3, 5). So, BM₂ = √(9 - 3)² + (1 - 5)² = 2√13

Midpoint of BC M₃(7, 5). So, AM₃ = √(7 - 1)² + (5 - 1)² = 2√13