Home > Geometry > Distance between Points

A triangle has corners at #(9 ,1 )#, #(2 ,4 )#, and #(5 ,8 )#. How far is the triangle's centroid from the origin?

Answer 1

Add all of the x coordinates of vertices, divide by 3, square that number do the same with the y coordinates add the two together and take the square root.

#d = sqrt(((9 + 2 + 5)/3)² + ((1 + 4 + 8)/3)²) #

#d = sqrt(((16)/3)² + ((13)/3)²) #

#d ~= 6.871#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Theodore Abad

To find the centroid of a triangle, you average the coordinates of its vertices.

The coordinates of the centroid are: [ (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}) ]

Given the coordinates of the vertices: [ (9, 1), (2, 4), (5, 8) ]

The centroid's coordinates are: [ (\frac{9 + 2 + 5}{3}, \frac{1 + 4 + 8}{3}) = (\frac{16}{3}, \frac{13}{3}) ]

The distance from the origin to the centroid is given by the distance formula: [ d = \sqrt{(x - 0)^2 + (y - 0)^2} ]

Substituting the centroid's coordinates: [ d = \sqrt{(\frac{16}{3})^2 + (\frac{13}{3})^2} ]

[ d = \sqrt{\frac{256}{9} + \frac{169}{9}} ]

[ d = \sqrt{\frac{425}{9}} ]

[ d \approx \frac{\sqrt{425}}{3} ]

[ d \approx 7.33 ]

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.