Question

If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is/(are) always rational points(s).

• A. Centroid
• B. Incentre
• C. Circumcentre
• D. Othocentre

Answer 1

The correct option is A Centroid

$C=(\frac{x_1+x_2+x_3}{3}$$,\frac{y_1+y_2+y_3}{3})$

$xϵR$

Let the slope be $m$,

Then, $m_{AD}=\frac{-1}{m_{BC}}$

$m_{AD}ϵR$

So, orthocentre $ϵR$

Hence, The coordinates of the orthocentre and centroid are rational.