Let X(a, p), Y(b, q) and Z(c, r) be the points such that a, b and c are in AP. If p, q and r are in AP, then the points X, Y and Z are
A.on a straight line✓ Correct
B.on a circle
C.on a parabola
D.the vertices of a triangle
Explanation
If a, b, c are in AP, then 2b = a + c, so b = (a+c)/2. If p, q, r are in AP, then 2q = p + r, so q = (p+r)/2. This means Y(b, q) = ((a+c)/2, (p+r)/2) is the midpoint of XZ. Therefore X, Y, Z are collinear, lying on a straight line.
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