Question

The vertices of a triangle are $A(1,2),B(5,7)$ and $C(11,13).$ Find the length of the median passing through vertex $A.$

Answer 1

$A(1,2),B(5,7),C(11,13)$

Median passes through midpoint of $BCi.e.,(\frac{5+11}{2},\frac{7+13}{2})=(8,10)$

Distancee between $2$ points is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}\sqrt{(8-1{)}^2+(10-2{)}^2}\sqrt{7^2+8^2}\sqrt{49+64}\sqrt{113}$