Question

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

(3, 1) and (9, 3)

Answer 1

Given: A = (3, 1) and B = (9, 3)

Let the point P be (x, y). So,
Area of triangle ABP = 0

\[\Rightarrow ∆ = \frac{1}{2}\begin{vmatrix}3 & 1 & 1 \\ 9 & 3 & 1 \\ x & y & 1\end{vmatrix} = 0\] 
\[ \Rightarrow 3\left( 3 - y \right) - 1\left( 9 - x \right) + 1\left( 9y - 3x \right) = 0\] 
\[ \Rightarrow 9 - 3y - 9 + x + 9y - 3x = 0\] 
\[ \Rightarrow - 2x + 6y = 0\] 
\[ \Rightarrow x = 3y\]