Question

The vertices of triangle are A(1,2) B(5,7) C(11,13) find the length of median passing through the vertex A

Answer 1

The median will bisects the side BC at (11+5/2=8,13+7/2=10).
Now distance between point (1,2)and (8,10) is root 113

Answer 2

Answer:

The length of median is 10.63 units.

Step-by-step explanation:

Given the vertices of triangle are A(1,2), B(5,7), C(11,13).

we have to find the length of median passing through the vertex A.

As the median pass through the mid-point of the side opposite to vertex i.e pass through mid-point of the side BC as it pass through the vertex A.

$\text{The mid point of line-segment joining the points (a,b) and (c,d) is }$

$(\frac{a+c}{2},\frac{b+d}{2})$

Now,

$\text{The mid point of line-segment joining the points B(5,7) and C(11,13) is }$

$(\frac{5+11}{2},\frac{7+13}{2})=(8,10)$

By distance formula

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The length of median i.e the distance between the points (1,2) and (8,10) is

$Distance=\sqrt{(8-1)^2+(10-2)^2}$

              $=\sqrt{49+64}=\sqrt{113}=10.63units$