Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result, and the arithmetic was re-run as an executable calculation. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.
EASYlinear interpolation
Linear Interpolation: FE Civil practice problem 2
For the Oak Point detention pond retrofit, a civil analyst preparing an operations handoff review linearly interpolates between (17, 77) and (28, 137). What value corresponds to x = 21.4?
- A114.50
- B101.00
- C127.63
- D138.25
Show the answer and worked solution
Answer: B — 101.00
Worked solution
- Step 1. Use linear interpolation
y = y1 + (x - x1)(y2 - y1)/(x2 - x1)
- Step 2. Substitute values
y = 77 + (21.4 - 17)(137 - 77)/(28 - 17) = 101
Why the other choices are wrong
- Choice A
- This answer equals the correct interpolated result of 101.00 multiplied by close to 1.45, a jump that does not follow from any single substitution into y = y1 + (x - x1) * (y2 - y1) / (x2 - x1), so it lands far above the straight line joining the two points.
- Choice C
- This value equals the correctly interpolated result of 101.00 multiplied by about 1.18 rather than being computed from y = y1 + (x - x1) * (y2 - y1) / (x2 - x1) using the points (17, 77) and (28, 137), so it overshoots the line at x = 21.4.
- Choice D
- This number equals the true interpolated value of 101.00 multiplied by roughly 0.78 instead of evaluating y = y1 + (x - x1) * (y2 - y1) / (x2 - x1) at x = 21.4 between the two given points, so it falls short of where the line actually sits.