# A triangle has corners at #(5 ,9 )#, #(4 ,1 )#, and #(3 ,8 )#. How far is the triangle's centroid from the origin?

##### 1 Answer

#### Explanation:

The centroid is the point where the triangles medians meet. A median is a line through a vertex to the midpoint of the opposite side. A triangle has three medians , but will will only need to find two of these to find the point of intersection, which is the centroid.

Chose two sides:

Let

Find the coordinates of the midpoints of these two sides:

The coordinates of the midpoint of a line are given by:

For

For

We now find the equations of two lines using midpoints and vertices.

For

Gradient:

Using point slope form of a line:

For

Gradient:

Solving simultaneously:

Coordinates of centroid:

To find the distance from the origin we use the distance formula:

PLOT: