Determine whether the following points are collinear A(-1, -1), B(0, 1), C(1, 3)
Determine whether the following points are collinear A(-1, -1), B(0, 1), C(1, 3)
A(–1, –1), B(0, 1), C(1, 3)
Slope of AB = \[\frac{1 - \left( - 1 \right)}{0 - \left( - 1 \right)} = \frac{2}{1} = 2\]
Slope of BC = \[\frac{3 - 1}{1 - 0} = \frac{2}{1} = 2\]
Slope of BC = \[\frac{3 - 1}{1 - 0} = \frac{2}{1} = 2\]
Slope of AB = Slope of BC = 2
Thus, the given points are collinear.
Explanation:-
The given points are A(-1, -1), B(0, 1), C(1, 3).
The slope of AB can be found using the formula:
slope of AB = (y2 – y1) / (x2 – x1)
Substituting the coordinates of A and B, we get:
slope of AB = (1 – (-1)) / (0 – (-1)) = 2/1 = 2
Similarly, the slope of BC can be found using the formula:
slope of BC = (y2 – y1) / (x2 – x1)
Substituting the coordinates of B and C, we get:
slope of BC = (3 – 1) / (1 – 0) = 2/1 = 2
Since the slope of AB is equal to the slope of BC, the points A, B, and C are collinear.
Chapter 5. Co-ordinate Geometry – Practice Set 5.3 (Page 121)