Determine whether the following points are collinearL(2, 5), M(3, 3), N(5, 1)
Determine whether the following points are collinearL(2, 5), M(3, 3), N(5, 1)
L(2, 5), M(3, 3), N(5, 1)
\[\text { Slope of LM } = \frac{3 - 5}{3 - 2} = \frac{- 2}{1} = - 2\]
\[\text { Slope of MN} = \frac{1 - 3}{5 - 3} = \frac{- 2}{2} = - 1\]
\[\text { Slope of LM } = \frac{3 - 5}{3 - 2} = \frac{- 2}{1} = - 2\]
\[\text { Slope of MN} = \frac{1 - 3}{5 - 3} = \frac{- 2}{2} = - 1\]
Slope of LM not equal to slope of MN. Thus, the given points are not collinear.
Explanation:-
To check if the points L(2, 5), M(3, 3), and N(5, 1) are collinear, we can find the slope of the line passing through any two of these points, and then check if the slope is the same for all pairs of points. If the slope is the same, the points are collinear; otherwise, they are not.
Slope of LM = (3 – 5)/(3 – 2) = -2/1 = -2
Slope of MN = (1 – 3)/(5 – 3) = -2/2 = -1
Since the slope of LM is not equal to the slope of MN, the points L(2, 5), M(3, 3), and N(5, 1) are not collinear.
Chapter 5. Co-ordinate Geometry – Practice Set 5.3 (Page 121)