Question

Find the equation of the line joining A(5,1), B(4,0) using determinants.

(a) 4x-y=4

(b) x-4y=4

(c) x-y=4

(d) x-y=0

This question was addressed to me in an interview.

Question is from Area of a Triangle topic in division Determinants of Mathematics – Class 12

Answer 1

Correct option is (c) x-y=4

The best I can explain: Let C(x,y) be a point on the line AB. Thus, the points A(5,1), B(4,0), C(x,y) are collinear. Hence, the area of the triangle formed by these points will be 0.

⇒Δ=\(\frac{1}{2}\begin{Vmatrix}5&1&1\\4&0&1\\x&y&1\end{Vmatrix}\)=0

Applying R1→R1-R2

\(\frac{1}{2}\begin{Vmatrix}1&1&0\\4&0&1\\x&y&1\end{Vmatrix}\)=0

Expanding along R1, we get

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

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

⇒x-y=4.