Using determinants, find the equation of the line joining the poi… - Vidyadip

Question

Using determinants, find the equation of the line joining the points:
(1, 2) and (3, 6)

✓

Answer

Given: a = (1, 2) and B = (3, 6)
Let the point p be (x, y). So,
Area of triangle ABP = 0
$\Rightarrow\triangle=\frac{1}{2}\begin{vmatrix}1&2&1\\3&6&1\\\text{x}&\text{y}&1\end{vmatrix}=0$
⇒ 1(6 - y) - 2(3 - x) + 1(3y - 6x) = 0
⇒ 6 - y - 6 + 2x + 3y - 6x = 0
⇒ 2y - 4x = 0
⇒ y = 2x

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