Drive the expression for the centraid of right angled triangle.
Answers
Answer:
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Explanation:
If you can show where the medians (the segment from a vertex to the midpoint of the other side of the right triangle) intersect each other, then this point of intersection is the CENTROID. To calculate this location, take 2/3 the distance from each vertex to the midpoint of the other side.
Answer:
If you can show where the medians (the segment from a vertex to the midpoint of the other side of the right triangle) intersect each other, then this point of intersection is the CENTROID. To calculate this location, take 2/3 the distance from each vertex to the midpoint of the other side.
Explanation:
Let ABC be a triangle with the vertex coordinates A( (x1, y1), B(x2, y2), and C(x3, y3). The midpoints of the side BC, AC and AB are D, E, and F, respectively. The centroid of a triangle is represented as “G.”
As D is the midpoint of the side BC, the midpoint formula can be determined as:
((x2+x3)/2, (y2+y3)/2)
We know that point G divides the median in the ratio of 2: 1. Therefore, the coordinates of the centroid “G” are calculated using the section formula.
To find the x-coordinates of G:
X = (2(x2+x3)/2 + 1.x1 )/ (2+1)
x= (x2+x3+x1)/3
x = (x1+x2+x3)/3
To find the y-coordinates of G:
Similarly, fo y-coordinates of the centroid “G.”
Y =(2(y2+y3)/2 + 1.y1 )/ (2+1)
y= (y2+y3+y1)/3
x = (y1+y2+y3)/3
Therefore, the coordinates of the centroid “G” is ((x1+x2+x3)/3 , (y1+y2+y3)/3 )
Hence, proved
Try This: Centroid Calculator