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If three points A, B and C are collinear and B lies between A and C, then,

- AB + BC = AC. AB, BC, and AC can be calculated using the distance formula.
- The ratio in which B divides AC, calculated using section formula for both the x and y coordinates separately will be equal.
- Area of a triangle formed by three collinear points is zero.

NOTES

**(I) Four points will form:**

(a) A **parallelogram** if it’s opposite sides is equal, but diagonals are unequal.

(b) A **rectangle** if opposite sides is equal and two diagonals are also equal.

(c) A **rhombus** if all the four sides are equal, but diagonals unequal,

(d) A **square** if all sides are equal and diagonals are also equal.

**(II) Three points will form:**

(a) An equilateral triangle if all the three sides are equal.

(b) An isosceles triangle if any two sides are equal.

(c) A right angled triangle if sum of square of any two sides is equal to square of the third side.

(d) A triangle if sum of any two sides (distances) is greater than the third side (distance).

**(III) Three points A, B and C are collinear or lie on a line if one of the following holds**

(i) AB + BC — AC

(ii) AC + CB AB

(iii) CA + AB CB.

Example

Find the distance of the point (-3, 4) from the x-axis.

Solution:

B(-3, 0), A (-3, 4)

Example.

If the points A(x, 2), B(-3, 4) and C(7, -5) are collinear, then find the value of x.

Solution:

When the points are collinear,

Example

In which quadrant the point P that divides the line segment joining the points A (2, -5) and B(5,2) in the ratio 2 : 3 lies?

Solution:

IV Quadrant

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