SSC CGL 2026 PYQ — Question 19

The correct answer is Option 2 i.e. ${10\over3}$ cm.

Let B = (0, 0), A = (6, 0), C = (0, 8)

In a right triangle, the orthocenter is at the vertex of the right angle.

So, H = B = (0, 0)

Centroid G $= \left( \frac{x_A + x_B + x_C}{3},\ \frac{y_A + y_B + y_C}{3} \right)$

$= \left( \frac{6+0+0}{3},\ \frac{0+0+8}{3} \right)$

$= \left( \frac{6}{3},\ \frac{8}{3} \right)$

$= \left(2,\ \frac{8}{3}\right)$

Length from G to H $= \sqrt{ (2-0)^2 + \left( \frac{8}{3} - 0 \right)^2 }$

$= \sqrt{ 4 + \frac{64}{9} }$

$=\sqrt{ \frac{100}{9} }$

= 10/3 cm