Math Questions and Answers

Start Your Free Trial

What is the centroid of the triangle with vertices (6, 4), ( 3,1) and (0, 4)?  

Expert Answers info

Tushar Chandra eNotes educator | Certified Educator

calendarEducator since 2010

write12,551 answers

starTop subjects are Math, Science, and Business

The centroid of a triangle is the point where the medians of the triangle meet. So we can find the centroid by determining the point of contact of two medians.

In the given triangle, the midpoint of (6, 4) and ( 3,1) is [( 6 + 3)/2 , (4 + 1)/2]. The equation of the line joining (0, 4) and ( 9/2 , 5/2) is

y – 4 = [( 4 – 5/2)/(0-9/2)]*(x – 0)

=> y – 4 = [(3/2) / (-9/2)]( x – 0)

=> -3 ( y – 4) = x

=> x + 3y – 12 = 0

The midpoint of ( 3,1) and (0, 4) is ( 3/2 , 5/2)

The line joining (6 , 4) and ( 3/2 , 5/2) is

y – 4 = [( 4 – 5/2)/(6 – 3/2)]( x – 6)

=> y – 4 = [( 3/2)/(9/2)]( x – 6)

=> 3(y – 4) = ( x – 6)

=> x - 3y + 6 = 0

We now need the point of intersection of x + 3y – 12 = 0 and x - 3y + 6 = 0.

Adding the two equations: 2x  - 6 = 0 or x = 3 and substituting x = 3 in x + 3y - 12 = 0 gives y = 3.

The centroid of the traingle is (3 , 3)

check Approved by eNotes Editorial