Show that the points `(b,c+a),(c,a+b) `and `(a,b+c)` are collinear

If a ,b ,c are the p t h ,q t h ,r t h terms, respectively, of an H P , show that the points (b c ,p),(c a ,q), and (a b ,r) are collinear.

If a ,b ,c are the p t h ,q t h ,r t h terms, respectively, of an HP , show that the points (b c ,p),(c a ,q), and (a b ,r) are collinear.

If a, b, c are distinct real numbers, show that the points (a, a^2), (b, b^2) and (c, c^2) are not collinear.

Prove that the points (a, b), (c, d) and (a-c, b-d) are collinear, if ad = bc.

Show that the points A(-3, 3), B(7, -2) and C(1,1) are collinear.

Using slopes, show that the points A(0,5) , B(3,2) and C(-1,6) are collinear.

Show that the points A(1,3,2),B(-2,0,1) and C(4,6,3) are collinear.

Show that the points A(6,4) , B(9,7) and C(11,9) are collinear.

Prove that the points (a ,b+c),(b ,c+a)a n d(c ,a+b) are collinear.

Show that the points (a,b,c)(b,c,a) and (c,a,b) are the vertices of an equilateral triangle.