Determine whether the following points are collinear D(-2, -3), E(1, 0), F(2, 1)
Determine whether the following points are collinear D(-2, -3), E(1, 0), F(2, 1)
D(–2, –3), E(1, 0), F(2, 1)
\[\text { Slope of DE } = \frac{0 - \left( - 3 \right)}{1 - \left( - 2 \right)} = \frac{3}{3} = 1\]
\[\text { Slope of DE } = \frac{0 - \left( - 3 \right)}{1 - \left( - 2 \right)} = \frac{3}{3} = 1\]
\[\text { Slope of EF } = \frac{1 - 0}{2 - 1} = \frac{1}{1} = 1\]
Slope of DE = Slope of EF = 1
So, the given points are collinear.
Explanation:-
The problem involves determining whether the given points D(-2, -3), E(1, 0), and F(2, 1) are collinear, or lie on a straight line.
To determine if the points are collinear, we can calculate the slope between each pair of points and see if they are equal.
The slope between two points can be found using the slope formula:
slope = (y2 – y1) / (x2 – x1)
Slope of DE: slope of DE = (0 – (-3)) / (1 – (-2)) = 3 / 3 = 1
Slope of EF: slope of EF = (1 – 0) / (2 – 1) = 1 / 1 = 1
Since the slope of DE is equal to the slope of EF, we can conclude that the points D, E, and F are collinear, and lie on the same straight line.
Therefore, the given points are collinear.
Chapter 5. Co-ordinate Geometry – Practice Set 5.3 (Page 121)