Determine whether the following points are collinear.. P(2, -5), Q(1, -3), R(-2, 3)
Determine whether the following points are collinear.. P(2, -5), Q(1, -3), R(-2, 3)
P(2, –5), Q(1, –3), R(–2, 3)
\[\text { Slope of PQ } = \frac{- 3 - \left( - 5 \right)}{1 - 2} = \frac{2}{- 1} = - 2\]
\[\text { Slope of PQ } = \frac{- 3 - \left( - 5 \right)}{1 - 2} = \frac{2}{- 1} = - 2\]
\[\text{ Slope of QR } = \frac{3 - \left( - 3 \right)}{- 2 - 1} = \frac{6}{- 3} = - 2\]
Slope of PQ = Slope of QR
So, the given points are collinear.
Explanation:- The given points are P(2, -5), Q(1, -3), and R(-2, 3).
To check whether these points are collinear, we can find the slopes of the lines passing through them. If the slopes are equal, then the points are collinear.
Slope of PQ: [\text{Slope of PQ }= \frac{-3 – (-5)}{1 – 2} = \frac{2}{-1} = -2]
Slope of QR: [\text{Slope of QR }= \frac{3 – (-3)}{-2 – 1} = \frac{6}{-3} = -2]
Since the slope of PQ is equal to the slope of QR, the given points P, Q, and R are collinear.
Chapter 5. Co-ordinate Geometry – Practice Set 5.3 (Page 121)