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This is sometimes referred to as center of mass, as well. If you could take the vector sum of all the torques produced by all of the 'point-masses' to this particular point they will net to zero. For simplicity, consider a weightless see-saw.
On the right side of the see-saw is a person weighing 100 pounds, who is 6 feet away from the pivot point. This produces (100 pounds force) x (6 feet ) = 600 foot-pounds force of torque, in the clockwise direction. On the other side of the see saw is a 200 pound person at 3 feet away from the pivot. This will produce (200 pounds force) x (3 feet ) = 600 foot-pounds force of torque, in the counter-clockwise direction. So the see-saw is balanced.
Now for each 'point-mass' (this is an infintessimaly small area with an associated small mass), a certain distance away from the centroid, there would be an equal mass the same distance away on the other side, but a vertex is farther away than the opposite side, so there will be two points, each at an angle from the centroid to a point which are a shorter distance, but add to balance the farther points. This is kind-of hard to explain without pictures.
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∙ 13y ago
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Why is the centroid of a triangle important?
It is the triangle's point of equilibrium or its point of balance.
The centroid of a triangle is the point where which part of the triangle intersect?
Medians
A point of concurrency of the medians of a triangle?
centroid
Where is the balance point of a triangle?
The centroid - which is where the medians meet.
What is the part of the triangle that is equidistant from the vertices of the triangle?
The centroid, which is the point where the medians meet.
Is the centroid the balancing oint in a triangle?
Yes
Centroid of a triangle?
centroid of a triangle lies at the point where the medians of the triangle intersect.
which statement is true the centroid and the circumcenter are the same point?
the centroid is the balance point of the triangle
Why is the centroid of a triangle important?
It is the triangle's point of equilibrium or its point of balance.
The centroid of a triangle is the point where which part of the triangle intersect?
Medians
The medians of a triangle are concurrent at what point?
Centroid
What is the point where the three medians of a triangle?
Centroid .
What is the Point of concurrency of the medians of a triangle?
The point of concurrency of the medians of a triangle is called the centroid. It is the point where all three medians intersect each other. The centroid divides each median into two segments, with the segment closer to the vertex being twice as long as the other segment.
Medians of a triangle are concurrent at this point?
Centroid
A point of concurrency of the medians of a triangle?
centroid
Point of intersection of medians in a triangle?
The point where the three medians of a triangle intersect is called the centroid of the triangle.
The point of concurrency of the medians of a triangle is called the?
The Centroid
