# MAT - Paper 2018 - Q1F

> Source: https://ollybritton.com/notes/maths/problems/mat/2018/q1f/ · Updated: 2021-10-27 · Tags: mat, notes, maths

## Flashcards

### Extreme lines of a stepping particle
##### If a particle can only move by a vector $<2, 1>$ or $<1, 2>$, what are the two "extreme" lines that the particle can get closest to??
$$
y = 2x
$$

$$
y = \frac{1}{2} x
$$
^extreme-lines-of-step-vectors

##### When thinking about something that can only move in certain ways (i.e. discrete steps or along certain angles), what is it sometimes constructive to do??
Visualise the areas of possibility by considering extreme cases.
^visualise-reachable-region-extremes

### Closest approach to a point
##### If a particle can only travel along the line $y = 2x$, how would you find the closest it can get to $(25, 75)$??
Finding where the line perpendicular and passing through $(25, 75)$ intersects the line.
^closest-approach-via-perpendicular

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