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

Even I also don't know the answer if you know please send me

Answer 2

Answer:

$\text{Length of median is }\sqrt{37}units$

Step-by-step explanation:

Given the two vertices are B(1,5) and C(-3,-1). we have to find the length of the median through the vertex A(5,1) drawn to the triangle ABC.

As a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side of triangle.

Therefore, the other coordinate of median is the mid-point of the two vertices B(1,5) and C(-3,-1) which is calculated by the mid-point formula

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})=(\frac{1+(-3)}{2},\frac{5+(-1)}{2})=(-1,2)$

By distance formula

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

Length of median is

$\sqrt{(5-(-1))^2+(1-2)^2}=\sqrt{36+1}=\sqrt{37}units$