Questions
If the vertices P, Q, R of a PQR are rational points, which of the following points of the PQR is (are) always rational point(s)?
a
centroid
b
incentre
c
circumcentre
d
orthocentre
detailed solution
Correct option is A
Let P≡x1,y1,Q≡x2,y2;R≡x3,y3, where xi,yi (i = 1, 2, 3) are rational numbers. Now, the centroid of ∆PQR isx1+x2+x33,y1+y2+y33which is rational point. Incentre, circumcentre and orthocentre depend on sides of the triangle which may not be rational even if vertices are so. For example, for P0,1 and Q1,0;PQ=2Talk to our academic expert!
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If an triangle circumcentre and orthocentre then the coordinates of the midpoint of the side opposite to A are
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