Determine whether the given points are collinear.
(3) L(1,2) , M(5,3) , N(8,6)
2. Determine whether the given points are collinear.
(3) L(1,2) , M(5,3) , N(8,6)
Answer:-
L(1,2), M(5,3) , N(8,6)
Slope of LM
[= frac{3 – 2}{5 – 1} = frac{1}{4}]
[= frac{3 – 2}{5 – 1} = frac{1}{4}]
Slope of MN = [frac{6 – 3}{8 – 5} = frac{3}{3} = 1]
Thus, the slope of LM not equal to slope MN.
So, the given points are not collinear.
Explanation:-
We can determine whether the given points are collinear by checking if the slopes between any two pairs of points are equal.
The slope of LM can be found as:
slope of LM = (y2 – y1)/(x2 – x1) = (3 – 2)/(5 – 1) = 1/4
The slope of MN can be found as:
slope of MN = (y2 – y1)/(x2 – x1) = (6 – 3)/(8 – 5) = 1
Since the slopes of LM and MN are not equal, the given points L, M, and N are not collinear.
Chapter 5. Co-ordinate Geometry – Problem set 5 (Page 122)