Question

value of
for which
Find the
(1 p) and (4,-2)
the
points (-5,1)
are
colinear.​

Answer 1

GIVEN :-

• The points are ( 1 , p ) , ( 4 , -2 ) and ( -5 , 1 ) .

• The points are collinear .

TO FIND :-

• Value of p .

SOLUTION :-

   Let the points be A( 1, p ) , B( 4 , -2 ) and C(-5,1) .

    We have ,

           $\bullet\sf \ x_1=1 \ , \ y_1=p\\\\\bullet \ x_2=4 \ , \ y_2=-2\\\\\bullet \ x_3=-5 \ , \ y_3 = 1$

   The points A , B and C are collinear .

    $\sf\therefore \ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)$  $=0$

     $\implies\sf 1(-2-1)+4(1-p)+-5(p-(-2))=0\\\\ \implies 1\times -3 +4-4p +-5p -10= 0 \\\\\implies -3+4-4p-5p-10=0\\\\\implies -9p-9 = 0\\\\\implies -9p=9\\\\\implies\bf p = -1$

 

 Value of p = -1