If points A (2,1)and B (a,b)and C(4,-1) are collinear and a-b=1,find the values of a and b?

If points A (2,1)and B (a,b)and C(4,-1) are collinear and a-b=1,find t

1.	If points A (2,1)and B (a,b)and C(4,-1) are collinear and a-b=1,find the values of a and b?
Answer» If the points A(- 2, 1), B(a, b) and C(4, 1) are collinear and a - b = 1, we have to find a and b.If three points are collinear, then area covered by given points = 0.{tex}\\therefore{/tex} Area = {tex}\\frac { 1 } { 2 } \\left[ x _ { 1 } \\left( y _ { 2 } - y _ { 3 } \\right) + x _ { 2 } \\left( y _ { 3 } - y _ { 1 } \\right) + x _ { 3 } \\left( y _ { 1 } - y _ { 2 } \\right) \\right]{/tex}=0Here,\xa0(x1, x2, x3) = (- 2, a, 4)and (y1, y2, y3) = (1, b, 1)Area ={tex}\\frac { 1 } { 2 } [ - 2 ( b - 1 ) + a ( 1 - 1 ) + 4 ( 1 - b ) ]{/tex}Area =\xa0{tex}\\frac { 1 } { 2 } [ - 2 b + 2 + 0 + 4 ( 1 - b ) ]{/tex}\xa00 = -3b + 3or, 3b = 3 or, b = 1Given, a - b = 1i.e, a - 1 = 1a = 2(a, b) = (2, 1)