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Centroid is considered one of the most asked concept.
16 Questions around this concept.
If the vertices of a triangle
are rational points, which of the following point(s) of the triangle is (are) always rational point(s)?
The coordinates of the middle points of the sides of a triangle are and
then the coordinates of its centroid is:
Centroid
A median is the line joining the mid-points of a side and the opposite vertex of a triangle.
Centroid of a triangle is the point of intersection of the three medians of the triangle. A centroid divides any median in the ratio 2:1.
The coordinates of the centroid of a triangle (G) whose vertices are A (x1, y1), B (x2, y2) and C(x3, y3), is given by
Note:
If D (a1, b1), E (a2, b2) and F (a3, b3) are the mid point of ΔABC, then centroid of triangle ABC is given by
Example
If Origin is the centroid of a triangle ABC, and the coordinates of other two vertices of the triangle are A (4, –3) and B (–5, 2), then find the coordinates of the third vertex.
Solution
Let point C is (α, β)
Coordinates of C are (1, 1)
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Mathematics for Joint Entrance Examination JEE (Advanced) : Coordinate Geometry
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July 04, 2019
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Last Date to Apply : 15th September | Campuses in Agartala, Aizawl, Ajmer, Aurangabad, Calicut, Imphal, Itanagar, Kohima, Gorakhpur, Patna & Srinagar
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