Question

The co-ordinates of vertices A, B, C of a
triangle A B C are (-1,3), (1, 1) and (5, 1)
respectively. Find the length of median
AD​

Answer 1

Answer:

Step-by-step explanation:

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