Question

prove that the points, ( 1 ,2),(4,-1),(-2, 5) are collinear ?​

Answer 1

Proof is in the attachment

Answer 2

Answer:

Co-ordinator of A (x1,y1) = (1,2)

Co-ordinator of B (x2,y2) = (4,-1)

Co-ordinator of C (x3,y3) = (-2,5)

Area of (∆ABC) =1/2 [x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]

=1/2 [ 1(-1-5) + 4(5-2) + -2(2+1)]

= 1/2 [ -6 + 12 -6 ]

= 1/2 [ 12 - 12]

= 1/2×0

= 0

Hence, the area of (∆ABC) is zero so the points are collinear.