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Centroid of a Triangle

Centroid of a triangle is the point of intersection of the lines joining the vertex of the triangle to the midpoint of the opposite sides.

The centroid G(x, y) of a ∆ ABC with vertices A(x1, y1), B(x2, y2) and C(x3, y3) is given by

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Area of a triangle is given by

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Note: If three points A, B and C are given, then

  • ABC is an equilateral triangle if AB = BC = AC.
  • ABC is an isosceles triangle if any two sides are equal.
  • ABC is a right angled triangle if the square of longest side is equal to the sum of the squares of the other 2 sides.

If 4 points A, B, C and D are given, then

  • ABCD is a square if AB = BC = CD = AD and the diagonals AC = BD.
  • ABCD is a rhombus if AB = BC = CD = AD and the diagonals are not equal.
  • ABCD is a rectangle if AB = CD and BC = AD and if the diagonals AC = BD.
  • ABCD is a parallelogram if AB = CD and BC = AD and the diagonals are not equal.


The midpoint of the line segment is (3, 2). If (5, 6) is one end, then find the other end.
Let the other end be (xy).
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If the points (0, 1), (3, –4) and (4, k) are collinear, then k = ?
We know that condition for collinearity is given by,
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If (2, 1), (5, 7) and (–1, 4) are the vertices of a triangle, then find the centroid of the triangle.
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Find the equation of the straight line passing through the points (–5, 2) and (6, –4).
The equation of the line joining two points (x1y1) and (x2y2) is given by
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What shape do the points A(4, – 1), B(6, 0), C(7, 2) and D(5, 1) form?
Let us calculate the lengths of all sides and diagonals.
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We can see that AB = BC = CD = AD and AC ≠ BD. Hence the given points form a rhombus.

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