The distance of the origin from the centroid of the triangle whose...

Let $AB ≡ x - 2y + 1 = 0 and AC ≡ 2x - y - 1 = 0$

So, A\left(1, 1\right)$</p><p>Now, altitude from$B$which is perpendicular to line$2x - y - 1 = 0 and which passes through \left(\dfrac{7}{3}, \dfrac{7}{3}\right)$is$BH = x + 2y - 7 = 0$,</p><p>Now intersection of$BH \text{ and } AB$will give point$B\left(3, 2\right)

Similarly, altitude$from C$ is $CH = 2x + y - 7 = 0 ⇒ C \left(2, 3\right)$

Centroid of $△ ABC = E\left(2, 2\right) \text{ and } OE = 2\sqrt{2}$

where $O$ is origin.