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Question

Determine whether the following points are collinear.
(1) A(–1, –1), B(0, 1), C(1, 3)

(2) D(–2, –3), E(1, 0), F(2, 1)

(3) L(2, 5), M(3, 3), N(5, 1)

(4) P(2, –5), Q(1, –3), R(–2, 3)

(5) R(1, –4), S(–2, 2), T(–3, 4)

(6) A(–4, 4), K2, 52, N (4, –2)

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Solution

(1) A(–1, –1), B(0, 1), C(1, 3)
Slope of AB = 1--10--1=21=2
Slope of BC = 3-11-0=21=2
Slope of AB = Slope of BC = 2
Thus, the given points are collinear.

(2) D(–2, –3), E(1, 0), F(2, 1)
Slopeof DE=0--31--2=33=1Slopeof EF=1-02-1=11=1
Slope of DE = Slope of EF = 1
So, the given points are collinear.

(3) L(2, 5), M(3, 3), N(5, 1)
Slopeof LM=3-53-2=-21=-2Slopeof MN=1-35-3=-22=-1
Slope of LM not equal to slope of MN. Thus, the given points are not collinear.

(4) P(2, –5), Q(1, –3), R(–2, 3)
Slope of PQ=-3--51-2=2-1=-2Slope of QR=3--3-2-1=6-3=-2
Slope of PQ = Slope of QR
So, the given points are collinear.

(5) R(1, –4), S(–2, 2), T(–3, 4)
Slope of RS=2--4-2-1=6-3=-2Slope of ST=4-2-3--2=2-1=-2
Slope of RS = Slope of ST
So, the given points are collinear.

(6) A(–4, 4), K2, 52, N (4, –2)
Slope of AK=52-4-2--4=-322=-34Slope of KN=-2-524--2=-34
Slope of AK=Slope of KN
Thus, the given points are collinear.

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