If the vertices of a triangle are having rational coordinates then its centroid, circumcentre and orthocentre are rational

Statement 2:

In any triangle, orthocentre, centroid and circumcentre are collinear and centroid divides the line joining orthocentre and circumcentre in the ratio 2:1

a)

Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1

b)

Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1

If the vertices of a triangle are having rational coordinates then its centroid, circumcentre and orthocentre are rational

Statement 2:

In any triangle, orthocentre, centroid and circumcentre are collinear and centroid divides the line joining orthocentre and circumcentre in the ratio 2:1

a)

Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1

b)

Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1

c)

Statement 1 is True, Statement 2 is False

d)

Statement 1 is False, Statement 2 is True

1 Answer

127 votes

Answer Key / Explanation : (c) -

(c)

Centroid is a rational point. Orthocentre is intersection point of two altitudes which will bear rational coefficients when expressed as straight line. So, orthocentre is also rational. Circumcentre is intersection point of two perpendicular bisectors which will bear rational coefficient when expressed as a straight line. So, circumcentre is also rational. But statement 2 is not true as in equilateral triangle all the centres coincide