A triangle has corners at #(6 ,7 )#, #(2 ,6 )#, and #(1 ,5 )#. How far is the triangle's centroid from the origin?

Question

A triangle has corners at #(6  ,7  )#, #(2   ,6  )#, and #(1   ,5  )#.  How far is the triangle's centroid from the origin?

Noah Atkinson · Accepted Answer

Distance between centroid and origin is
d = sqrt5 = 2.2361

Coordinates of centroid: #x = (x1 + x2 + x3)/3, y = (y1 + y2 + y3)/3# #x = (6+2+1)/3=3# #y = (7+6+5)/3 = 2# Coordinates of centroid of the triangle (1,2)# Coordinates of origin (0,0). Distance between centroid and origin is #d = sqrt((1-0)^2+(2-0)^2) = sqrt5 = 2.2361#

Ella Armstrong · Answer

undefined To find the centroid of a triangle with vertices at coordinates (x1, y1), (x2, y2), and (x3, y3), you can use the formula:

Centroid = ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3)

Substitute the coordinates of the vertices into the formula:

Centroid = ((6 + 2 + 1) / 3, (7 + 6 + 5) / 3)

Centroid = ((9) / 3, (18) / 3)

Centroid = (3, 6)

The distance between the centroid and the origin (0, 0) can be calculated using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Substitute the coordinates of the centroid and the origin into the formula:

Distance = √((3 - 0)^2 + (6 - 0)^2)

Distance = √(9 + 36)

Distance = √45

Distance ≈ 6.71

So, the distance between the centroid of the triangle and the origin is approximately 6.71 units.