The vertices of a triangle are (6, 6), (0, 6) and (6, 0). The distance between origin and its centroid is

The centroid of a triangle is the point where the medians of the triangle intersect. The medians of a triangle are the lines from a vertex to the midpoint of the opposite side. The centroid is also the average of the x-coordinates and the y-coordinates of the vertices.

Step 1: Find the x-coordinate of the centroid The x-coordinate of the centroid is the average of the x-coordinates of the vertices. So, add up the x-coordinates of the vertices and divide by 3.

(6 + 0 + 6) / 3 = 4

Step 2: Find the y-coordinate of the centroid The y-coordinate of the centroid is the average of the y-coordinates of the vertices. So, add up the y-coordinates of the vertices and divide by 3.

(6 + 6 + 0) / 3 = 4

So, the centroid of the triangle is at (4, 4).

Step 3: Find the distance from the origin to the centroid The distance from the origin (0, 0) to the centroid (4, 4) can be found using the distance formula, which is √[(x2-x1)² + (y2-y1)²].

√[(4-0)² + (4-0)²] = √[16 + 16] = √32 = 4√2

So, the distance from the origin to the centroid of the triangle is 4√2 units.