Question

Find the equation of the line joining A (1, 3) and B (0, 0) using determinants and find k if D (k, 0) is a point such that area of ∆ABD is 3 sq.units.

Answer 1

Let P(x, y) be any point on line AB. Then,

Area of ∆ABP = 0

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

 ⇒ \(\frac{1}{2}\) [1 (0 - y) - 3(0 - x) + 1(0 - 0)] = 0

⇒ 3x - y = 0

which is the required equation of AB.

Now, area ∆ABD = 3 sq. units

⇒ 1(0 - 0) - 3(0 - k) + 1(0 - 0) = ± 6

⇒ 3k = ± 6

Thus, k = ± 2