# Coordinate Geometry-17

### From Homeworkwiki

**Examine the set of points (1/2, -2), (-2, 1/3), (5/2, 0) for collinearity.**

**Solution:** If three points are collinear, then the area of the triangle formed by the points is equal to zero.

Let (x_{1}, y_{1}) = (1/2, -2); (x_{2}, y_{2}) = (-2, 1/3); (x_{1}, y_{1}) = (5/2, 0)

Area of Triangle = ± 1/2 [ x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) +

x_{3} (y_{1} - y_{2}) ]

= ± 1/2 [1/2 (1/3 - 0) - 2(0 + 2) + 5/2 (-2 - 1/3)] = + / - 1/2 [- 58 / 6] = 29 / 6

Therefore, the three points are not collinear.

**Note** If (1/2, -2), (-2, 1/3), (5/2, 0) be denoted by A, B. C.

We can also show that the sum of any line segments is not equal to the third segment.