Question

Find the coordinates of the centroid of the triangle with the vertices A(-6,8) , B(-3,1) and C(0,3)

Answer 1

(-3, 4)

Step-by-step explanation:

The centroid is the intersection of the median of a triangle. The medians are segments that go from each vertex to the midpoint of the opposite side.

To find the midpoints of each side, we will use the following

`((x_1+x_2)/(2),(y_1+y_2)/(2)_{})_{}`

Where (x1, y1) and (x2, y2) are the coordinates of the two vertexes.

So, the midpoint of side AB can be calculated by replacing (x1, y1) by (-6, 8) and (x2, y2) by (-3, 1), then

`((-6+(-3))/(2),(8+1)/(2)_{})=((-9)/(2),(9)/(2))=(-4.5,4.5)`

The midpoint of side BC that goes from B(-3, 1) to C(0, 3) is

`((-3+0)/(2),(1+3)/(2))=((-3)/(2),(4)/(2)_{})=(-1.5,2)`

And the midpoint of side AC that goes from A(-6, 8) to C(0, 3) is

`((-6+0)/(2),(8+3)/(2))=((-6)/(2),(11)/(2))=(-3,5.5)`

So, we can draw the triangle and the medians as follows:

Therefore, the coordinates of the centroid are (-3, 4)