Question

Using determinants, find the equation of the line joining the points

(1, 2) and (3, 6)

Answer 1

Given: A  =  (1, 2) and B  =  (3, 6)

Let the point P be (x, y).  So,

Area of triangle ABP = 0

\[\Rightarrow ∆ = \frac{1}{2}\begin{vmatrix}1 & 2 & 1 \\ 3 & 6 & 1 \\ x & y & 1\end{vmatrix} = 0\] 
\[ \Rightarrow 1\left( 6 - y \right) - 2\left( 3 - x \right) + 1\left( 3y - 6x \right) = 0\] 
\[ \Rightarrow 6 - y - 6 + 2x + 3y - 6x = 0\] 
\[ \Rightarrow 2y - 4x = 0\] 
\[ \Rightarrow y = 2x\]