SOLUTION: Find the lengths of the medians of the triangle with vertices A(1, 3), B(2, 6), and C(8, 1). (A median is a line segment from a vertex to the midpoint of the opposite side. Round y

Algebra ->  Coordinate-system -> SOLUTION: Find the lengths of the medians of the triangle with vertices A(1, 3), B(2, 6), and C(8, 1). (A median is a line segment from a vertex to the midpoint of the opposite side. Round y      Log On


   

Question 888849: Find the lengths of the medians of the triangle with vertices A(1, 3), B(2, 6), and C(8, 1). (A median is a line segment from a vertex to the midpoint of the opposite side. Round your answers to one decimal place.)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the location of the median, find the midpoints of the line segments.
x%5BAB%5D=%28x%5BA%5D%2Bx%5BB%5D%29%2F2=%281%2B2%29%2F2=3%2F2
y%5BAB%5D=%28y%5BA%5D%2By%5BB%5D%29%2F2=%283%2B6%29%2F2=9%2F2
x%5BAC%5D=%28x%5BA%5D%2Bx%5BC%5D%29%2F2=%281%2B8%29%2F2=9%2F2
y%5BAC%5D=%28y%5BA%5D%2By%5BC%5D%29%2F2=%283%2B1%29%2F2=4%2F2=2
x%5BBC%5D=%28x%5BB%5D%2Bx%5BC%5D%29%2F2=%282%2B8%29%2F2=10%2F2=5
y%5BBC%5D=%28y%5BB%5D%2By%5BC%5D%29%2F2=%286%2B1%29%2F2=7%2F2
Then to find the length of the median, find the distance from the midpoint to the opposite vertex.
AB-C

D%5BAB-C%5D=sqrt%28218%29%2F2
.
.
.
AC-B
D%5BAC-B%5D%5E2=%289%2F2-2%29%5E2%2B%282-6%29%5E2=%285%2F2%29%5E2%2B%28-4%29%5E2=89%2F4
D%5BAC-B%5D=sqrt%2889%29%2F2
.
.
.
BC-A
D%5BBC-A%5D%5E2=%285-1%29%5E2%2B%287%2F2-3%29%5E2=%284%29%5E2%2B%281%2F2%29%5E2=65%2F4
D%5BBC-A%5D=sqrt%2865%29%2F2