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  • For what value of , are the points   and

For what value of p, are the points (2,1),(p,-1)  and (-1,3) collinear ?

 

 

Answers (1)

Points \Rightarrow (2,1);\; (p,-1);\; (-1,3)

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

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

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

                  =\frac{1}{2}\left [ -8+2p-2 \right ]

                    =\frac{1}{2}\left [ 2p-10 \right ]=0    

                    \Rightarrow 2p=10

                    \Rightarrow p=5

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Safeer PP

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