General ScienceMadrid 2026Question 2A
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Problem statement
Given the plane $\pi: 2x+2y-z=13$ and the line $$r\equiv\dfrac{x-2}{1}=\dfrac{y}{1}=\dfrac{z}{4}.$$
a) (1 mark) Find the reflection (mirror image) of the point $P(2,0,0)$ in the plane $\pi$.
b) (1 mark) Answer only one of the following two parts:
b1) Find the distance between the plane $\pi$ and the line $r$.
b2) Find an equation of the plane that contains the line $r$ and is orthogonal to the plane $\pi$.
Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Mathematics · Question 3. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.What this lesson answers
- What do the equations tell us before any calculation?
- How do we construct the reflection of a point in a plane?
- Does it make sense to talk about the distance between this line and this plane?
- Why is one point of the line enough to measure the distance?
- What does a plane need in order to be determined?
- Another route for each part: does it give the same?
- The answers and how to check them
- Common mistakes to avoid
- Exam tips
- For top marks
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