Question

Find the lengths of the medians AD and BE of ∆ABC whose vertices are A(7, -3), B(5, 3) and C(3, -1).

Answer 1

Vertices of ∆ABC are A(7, -3), B(5, 3) and C(3, -1).

From figure: BE and AD are the medians of triangle.

Find Coordinates of E and D:

Coordinates of E

(3+7/2, -1-3/2)

= (5, -2)

Coordinate of D =

(3+5/2, -1+3/2)

(4, 1)

Find AD and BE using distance formula:

AD = √{(x₂ - x₁)² + (y₁ - y₂)²}

= √{(7-4)² + (3+1)²}

= √(3² + 4²)

= √(9 + 16)

= √25

= 5 units

and BE = √{(5-5)² + (3+2)2} 

= √(0² + 5²)

=√25 

= 5 units

Therefore, BE = 5 units and AD = 5 units (both are equal).