If the points ( - 5, ,1), ,(p, ,5) and (10, ,7) are collinear, th… - Vidyadip

MCQ

If the points $( - 5,\,1),\,(p,\,5)$ and $(10,\,7)$ are collinear, then the value of $p$ will be

✓
$5$
B
$3$
C
$4$
D
$7$

✓

Answer

Correct option: A.

$5$

a
(a) $\frac{1}{2}\,\left| {\,\begin{array}{*{20}{c}}{ - 5}&1&1\\p&5&1\\{10}&7&1\end{array}\,} \right| = \,0\,\,$

$\Rightarrow \,\,\left| {\,\begin{array}{*{20}{c}}{ - 5}&1&1\\p&5&1\\{10}&7&1\end{array}\,} \right| = \,0\,$

$ \Rightarrow \,\,10 - (p - 10) + (7p - 50) = 0\,\,$

$\Rightarrow \,\,p = 5$.

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