Determine whether the given points are collinear. (1) A(0,2) , B(1,-0.5), C(2,-3)
2. Determine whether the given points are collinear.
(1) A(0,2) , B(1,-0.5), C(2,-3)
A(0,2), B(1,–0.5), C(2,–3)
Slope of AB = \[\frac{- 0 . 5 - 2}{1 - 0} = \frac{- 2 . 5}{1} = - 2 . 5\]
Slope of BC = \[\frac{- 3 - \left( - 0 . 5 \right)}{2 - 1} = \frac{- 2 . 5}{1} = - 2 . 5\]
So, the slope of AB = slope of BC.
Point B lies on both the lines.
Hence, the given points are collinear.
Explanation:-
To determine whether the given points are collinear, we need to check whether the slope of the line passing through any two of the three points is equal to the slope of the line passing through the other two points.
Let’s take the points A and B first. The slope of the line passing through A and B is:
[\frac{-0.5 – 2}{1 – 0} = -2.5]
Now, let’s take the points B and C. The slope of the line passing through B and C is:
[\frac{-3 – (-0.5)}{2 – 1} = -2.5]
Since the slopes of the lines passing through AB and BC are equal, we can conclude that the given points A, B, and C are collinear.
Chapter 5. Co-ordinate Geometry -Problem Set 5 (Page 122)