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

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

A

5

B

3

C

4

D

7

Answer

5

Explanation

Solution

12∣−511p511071∣=0⇒∣−511p511071∣=0\frac { 1 } { 2 } \left| \begin{array} { c c c } - 5 & 1 & 1 \\ p & 5 & 1 \\ 10 & 7 & 1 \end{array} \right| = 0 \Rightarrow \left| \begin{array} { c c c } - 5 & 1 & 1 \\ p & 5 & 1 \\ 10 & 7 & 1 \end{array} \right| = 0 ⇒10−(p−10)+(7p−50)=0⇒p=5\Rightarrow 10 - ( p - 10 ) + ( 7 p - 50 ) = 0 \Rightarrow p = 5 .