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The value of p, for which the points A(3,1),B(5,p) and C(7,-5) are collinear, is 
Option: 1 -2
Option: 2 2
Option: 3 -1
Option: 4 1

Answers (1)

Points \Rightarrow (3,1);\; (5,p);\; (7,-5)

The points will be colinear if the area of the triangle formed by the three points is zero.

Area of triangle

\Delta =\frac{1}{2}\left [ x_{1}[y_{2}-y_{3}]+x_{2}[y_{3}-y_{1}]+x_{3}(y_{1}-y_{2}) \right ]

Here it is

  \frac{1}{2}\left [ 3(p+5)+5(-6)+7(1-p) \right ]=0

\\3p+15-30+7-7p=0\\-4p=8\\p=-2

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Safeer PP

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