Passage: Let X(a,p) , Y(b,q) and Z(c,r) be the points such that a , b and c are in AP. Question: If p , q and r are not in AP and b=c , then the line joining the points X , Y and Z is parallel to

Step-by-step solution

Given that a , b , and c are in AP, we have 2b = a + c . It is also given that b = c . Substituting this into the first equation gives 2b = a + b , which implies a = b . Therefore, a = b = c . The coordinates of the points become X(a, p) , Y(a, q) , and Z(a, r) . Since the x -coordinates of all three points are equal, they lie on the vertical line x = a . This line is parallel to the y -axis. Answer: y -axis