Question

find the value value of P for which the point (-5,4) (2,p) and (-3,0) are collinear​

Answer 1

Answer:

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Answer 2

Given:

Three points $\[A\left( { - 5,4} \right),B\left( {2,P} \right)\]$ and $\[C\left( { - 3,0} \right)\]$

Solution:

Know that the points $\[A\left( {{x_1},{y_1}} \right),B\left( {{x_2},{y_2}} \right)\]$ and $\[C\left( {{x_3},{y_3}} \right)\]$ are said be collinear if-

$\[{x_1}\left( {{y_2} - {y_3}} \right) + {x_2}\left( {{y_3} - {y_1}} \right) + {x_3}\left( {{y_1} - {y_2}} \right) = 0\]$

Put values And evaluate P,

$\[\begin{array}{l} - 5\left( {p - 0} \right) + 2\left( {0 - 4} \right) - 3\left( {4 - p} \right) = 0\\ \Rightarrow - 5p + 10 - 8 + 3p = 0\\ \Rightarrow 2p = 2\\ \Rightarrow p = 1\end{array}\]$

Hence, the required value of p is 1.