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)
Answer:-
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)