Question

If A (-1,3), B(1,-1) and C(5,1) are the vertices of triangle ABC. Find the sum of length of medians through A and C​

Answer 1

Coordinates of A≡(−1,3)

Coordinates of B≡(1,−1)

Coordinates of C≡(5,1)

The median through the vertex C will meet at the mid point of AB.

Coordinate of mid-point on AB=(

2

(−1)+1

,

2

3+(−1)

)=(0,1)

Now,

Length of median through vertex C= Distance between (5,1) and (0,1)

Therefore,

Length of median =

(0−5)

2

+(1−1)

2

⇒ Length of median =

(5)

2

=5 units

Hence the length of median through the vertx C is 5 units.