From point to point

Can you combine vectors to get from one point to another?

Age

14 to 16

Challenge level

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

Problem

How can you get from $(10,66)$ to $(20,12)$

using only integer multiples of the vectors

$

(\begin{matrix} 2 \\ - 3 \end{matrix})

$ and $

(\begin{matrix} 3 \\ 2 \end{matrix})

$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.