Question
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
NDA
Mathematics
Sequences and Series
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. y-axis
- B. x-axis
- C. y=x
- D. y=-x
Answer
A. y-axis
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
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