Question

Find the equation of the line joining A(2,1) and B(6,3) using determinants.

(a) 2y-x=0

(b) 2y-x=0

(c) y-x=0

(d) y-2x=0

This question was posed to me in an internship interview.

My question is from Area of a Triangle topic in chapter Determinants of Mathematics – Class 12

Answer 1

Correct choice is (a) 2y-x=0

The best explanation: Let C(x,y) be a point on the line AB. Thus, the points A(2,1), B(6,3), C(x,y) are collinear. Hence, the area of the triangle formed by these points will be 0.

⇒Δ=\(\frac{1}{2}\begin{Vmatrix}2&1&1\\6&3&1\\x&y&1\end{Vmatrix}\)=0

Expanding along C3, we get

\(\frac{1}{2}\) {1(6y-3x)-1(2y-x)+1(6-6)}=0

\(\frac{1}{2}\) {6y-3x-2y+x}=\(\frac{1}{2}\) {4y-2x}=0

⇒2y-x=0