First slide

Equation of line in Straight lines

Question

The image of the centroid of the triangle whose ortho centre is at origin and the circum centre at $(3, 3)$ in the line which is equally inclined with axes in the first quadrant is

Moderate

A

$(2, 2)$
B

$(- 2, - 2)$
C

$(4, 4)$
D

$(- 2, - 4)$

Solution

In any triangle the centroid $G$ divides the line segment joining ortho center $O$ and the circum centre $S$ in the ratio $2 : 1$
It implies
$\begin{matrix} G = (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}) \\ = (\frac{2 (3) + 1 (0)}{1 + 2}, \frac{2 (3) + 1 (0)}{1 + 2}) \\ = (2, 2) \end{matrix}$
Equation of the line which is equally inclined, means making equal angles with axes in the first quadrant is $x = y$
The image of the point $P (x_{1}, y_{1})$ in the line $x = y$ is $(y_{1}, x_{1})$
The image of $G = (2, 2)$ in the line $x = y$ is $(2, 2)$

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