Determine whether the points are collinear.

(1) A(1, -3), B(2, -5), C(-4, 7)

(2) L(-2, 3), M(1, -3), N(5, 4)

(3) R(0, 3), D(2, 1), S(3, -1)

(4) P(-2, 3), Q(1, 2), R(4, 1)

If Three points (a,b), (c,d), (e,f) are collinear then the area formed by the triangle by the three points is zero.

Area of a triangle = ...(1)

1.
(a,b) = (1,-3)

(c,d) = (2,-5)

(e,f) = (-4,7)

Area =

Area = = 0

Hence the points are collinear.

2.

(a,b) = (-2,3)

(c,d) = (1,-3)

(e,f) = (5,4)

Area =

Area =

Hence the points are not collinear.

3.
(a,b) = (0,3)

(c,d) = (2,1)

(e,f) = (3,-1)

Area =

Area =

Hence the points are non collinear.

4.

(a,b) = (-2,3)

(c,d) = (1,2)

(e,f) = (4,1)

Area =

Area =

Hence the points are collinear.