If the points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_1 + x_2, y_1 + y_2)$ are collinear, then $x_1y_2$ is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $x_2y_1$ ##
When the points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_1 + x_2, y_1 + y_2)$ are collinear in the cartesian plane then
$\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_1 + x_2 & y_1 + y_2 & 1 \end{vmatrix} = 0$
$\Rightarrow 1 \cdot (x_2y_1 + x_2y_2 - x_1y_2 - x_2y_2) - 1(x_1y_1 + x_2y_1 - x_1y_1 - x_1y_2) + (x_1y_2 - x_2y_1) = 0$
$x_1y_2 = x_2y_1$