Question

find the length of the median through the vertex a 5,1 drawn to the triangle abc where other two vertices are B 1,5 and C - 3, 1

Answer 1

here it is , the answer is 5 units!

Answer 2

Answer:

The length of median through the vertex A is  $2\sqrt{10}units$.

Step-by-step explanation:

The vertices of triangle are A(5,1), B(1,5) and C(-3,1).

A median through the vertex divides the opposite side in two equal parts.

The median is drawn through the vertex A, therefore it divides the sides BC in two equal parts.

The midpoint of BC is

$M=(\frac{1+(-3)}{2},\frac{5+1}{2})=(-1,3)$

The endpoints of the median are (5,1) and (-1,3). The length of median is

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

$AM=\sqrt{(-1-5)^2+(3-1)^2}$

$AM=\sqrt{36+4}$

$AM=\sqrt{40}$

$AM=2\sqrt{10}$

Therefore the length of median through the vertex A is  $2\sqrt{10}units$.