Question

For what value of p, the points (-5, 1), (1, p) and (4, -2) are collinear *
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Answer 1

$\huge {\underline {\underline {\mathbb {\red {Answer:-}}}}}$

Let (-5,1) be the co-ordinates of A and (1,p) the co-ordinates of B and (4 , -2) the co-ordinates of C

IF THREE POINTS ARE COLLINEAR THEN SLOPE OF ANY TWO PAIRS OF POINTS WILL BE EQUAL

slope of AB = Slope of BC

$=> \frac {p-1}{1-(-5)} = \frac {-2-p}{4-1}$

$=> \frac {p-1}{6} = \frac {-2-p}{3}$

$=> 3(p-1) = 6(-2-p)$

$=> 3p-3=-12-6p$

$=> 3p+6p =-12+3$

$=> 9p = -9$

$=>p= \frac {-9}{9}$

$\therefore p = -1$