Straight Line and Pair of Straight Lines 1 Question 31

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

$(1998,2$ M)

(a) centroid

(b) incentre

(c) circumcentre

(d) orthocentre

(A rational point is a point both of whose coordinates are rational numbers)

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Solution:

  1. Since, the coordinates of the centroid are $\frac{x _1+x _2+x _3}{3}, \frac{y _1+y _2+y _3}{3}$, then the centroid is always a rational point.


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