If (a,b) is mid point of line segment joining the points A(10,-6), B(k,4) and a-2b =16,then find the value of k and the distance AB.

Important Points of: 

  1. Collinear Points: Three points A, B, C are said to be collinear if they lie on the same straight line.
  2. Test for Collinearity of three points: In order to show that three given points A, B, C are collinear, we find distance AB, BC and AC. If the sum of any two of these distances is equal to the third distance then the given points are collinear.
  3. Centroid of a triangle: The point of intersection of the medians of a triangle is called its centroid.
  4. Coordinate of Centroid :(x1+x2+x3)/3, (y1+y2+y3)/3.
  5. Properties of various types of Quadrilaterals:
  •  Rectangle: if its opposite sides are equal and the diagonals are equal.
  • Square: if all its sides are equal and the diagonals are equal.
  • Parallelogram but not a rectangle: if its opposite sides are equal and the diagonal are not equal.
  • Rhombus bur not a Square: if all sides are equal and diagonals are not equal. 

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