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Consider the Centroid Theorem.
(3,2)
Let's begin by plotting the triangle in a coordinate plane using the given coordinates.
To find the centroid of a triangle, we first need to determine the midpoint of each side. We can do that using the Midpoint Formula.
| Side | Points | M(x_1+x_2/2,y_1+y_2/2) | Midpoint |
|---|---|---|---|
| JK | ( -1,2), ( 5,6) | M(-1+ 5/2,2+ 6/2) | M(2,4) |
| JL | ( -1,2), ( 5,-2) | N(-1+ 5/2,2+( -2)/2) | N(2,0) |
| KL | ( 5,6), ( 5,-2) | P(5+ 5/2,6+( -2)/2) | P(5,2) |
Let's add these midpoints to our graph.
According to the Centroid Theorem, the centroid of a triangle is two-thirds the distance from each vertex to the midpoint of the opposite side. Note that the midpoint P(5,2) shares a y-coordinate with the vertex J. This allows us to calculate the distance as the difference between x-coordinates. 2/3( P_x- J_x)=2/3( 5-( -1))=4 This calculation tells us that the centroid is 4 units from vertex J along the median. In this case, the median is JP.
We can see that the coordinates of the centroid are (3,2).
