SumNinja

Describe a move with a vector

About 2 min

A point tells you where something is. A vector tells you how to move. Subtract start from target to find that change.

A game piece starts at (−1, 2) and must reach (3, 5). A point lists left-right position first, then height. The move between those points is a vector. Its two numbers tell you how far to go left or right, then up or down.

A is the start; B is the target

Follow the grid from A to B: four right and three up. The arrow shows the single move joining those points.

Find the move from A to B

Start A = (−1, 2); target B = (3, 5).

  1. Find the left-right change

    3−(−1)=43-(-1)=4

    Move from one left of zero to three right of zero. That takes four units to the right.

  2. Find the up-down change

    5−2=35-2=3

    The height rises from two to five. That takes three units up.

  3. Combine the two changes

    [43]\begin{bmatrix}4\\3\end{bmatrix}

    The pair (4, 3) and the column show the same vector. Left-right change comes first. Add that move to A and you reach B.

A move is not a fixed place

The point (3, 5) names a location. The vector (4, 3) names a change. Use that vector from (10, 10), and you end at (14, 13). The move stays the same even when the start changes.

A negative first number means left; a negative second number means down. For each part, use target minus start. Reversing that order makes a move back toward the start.

This start-to-end change also has a name: displacement. It records the overall move, even if the piece took a longer route to get there.

Try it yourself

Work out an answer and explain your reasoning. Then check the explanation.

Read a signed move

[−32]\begin{bmatrix}-3\\2\end{bmatrix}

Where would this vector move a piece? Name both changes.

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[−32]\begin{bmatrix}-3\\2\end{bmatrix}

The first number is negative, so move left. The second is positive, so move up.

Find a displacement

[−13]−[2−1]\begin{bmatrix}-1\\3\end{bmatrix}-\begin{bmatrix}2\\-1\end{bmatrix}

Find the move, then check which point you reach when you use it from the start.

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[−34]\begin{bmatrix}-3\\4\end{bmatrix}

Target minus start gives −1 − 2 = −3 and 3 − (−1) = 4. Add the move to the start to check.

Find a move with new start and target points

Give the left-right change first and the up-down change second. Check that your answer takes the start to the target.

2-minute practice · keep going after mistakes · opens in a new tab

Try finding a move