If points A (2,1)and B (a,b)and …
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Sia ? 6 years, 4 months ago
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}=0
Here, (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 = {tex}\frac { 1 } { 2 } [ - 2 b + 2 + 0 + 4 ( 1 - b ) ]{/tex}
0 = -3b + 3
or, 3b = 3 or, b = 1
Given, a - b = 1
i.e, a - 1 = 1
a = 2
(a, b) = (2, 1)
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