Learn with Alicia← Secondary Maths

Senior 2 • Vectors and Translation • Showcase mission

The Missing First-Aid Box

Sports Day begins in less than an hour, but the first-aid box is in the wrong place. Use vectors to give one route that nobody can misunderstand.

⏱ 55–70 minutes✎ Pencil and paper★ Explain every answer
Open the mission →
YOUR MISSION PROGRESS • 0 OF 15 PRACTICE QUESTIONS SOLVED0%

The situation

The clinic has supplies—but no exact route.

The school field has been drawn on a coordinate grid. The equipment store is at A(2, 1), while the first-aid tent is at B(6, 4). A volunteer wrote 'move over and up' on the route card—but that instruction is not exact enough.

⚠ THE PROBLEM YOU MUST SOLVE

How far right and how far up must the box move from A to B?

Your job: describe the movement as a vector, use it to translate other points, and check that the route ends at the first-aid tent.

Foundation • A vector describes movement

Direction and distance belong together.

A vector tells us how far an object moves horizontally and vertically. We write the horizontal movement first, then the vertical movement. Right and up are positive; left and down are negative.

FIRST COMPONENT

Horizontal movement

Compare the x-coordinates. From x = 2 to x = 6 is 4 units to the right, so the first component is +4.

SECOND COMPONENT

Vertical movement

Compare the y-coordinates. From y = 1 to y = 4 is 3 units up, so the second component is +3.

THE CHECK

Add to the start

A(2, 1) + (4, 3) = (6, 4). The result is B, so the vector reaches the correct destination.

Worked example • Follow the reasoning

Find the vector from A(2, 1) to B(6, 4).

Use destination minus starting point. Keep x with x and y with y.

1
HORIZONTAL6 − 2 = 4

Move 4 units right.

2
VERTICAL4 − 1 = 3

Move 3 units up.

3
WRITE AND CHECKAB = (4, 3)

(2, 1) + (4, 3) = (6, 4).

QUICK CHECK 1

What vector moves P(1, 2) to Q(5, 7)?

QUICK CHECK 2

Translate R(−1, 2) by the vector (5, −3). Where does it land?

QUICK CHECK 3

What is (3, 2) + (−1, 4)?

QUICK CHECK 4

What vector moves A(3, −2) to B(−1, 5)?

QUICK CHECK 5

Translate C(2, −3) by (4, 6).

QUICK CHECK 6

Which vector leaves every point unchanged?

QUICK CHECK 7

What is the opposite of the vector (3, −5)?

QUICK CHECK 8

Combine the movements (2, 1) and (3, −4).

QUICK CHECK 9

A translation moves a triangle. What stays the same?

QUICK CHECK 10

What does the first component −6 mean?

QUICK CHECK 11

What does the second component +4 mean?

QUICK CHECK 12

Find the vector from P(−2, 4) to Q(−2, −3).

QUICK CHECK 13

A point moves twice by (2, 3). What is the total movement?

QUICK CHECK 14

Where does O(0, 0) land after translation by (−5, 2)?

QUICK CHECK 15

Which vector returns B to A if AB = (4, 3)?

Final scenario challenge

Which route card reaches the first-aid tent?

The box begins at A(2, 1) and must finish at B(6, 4). Choose the exact instruction.

Explain your thinking

Why is a vector safer than saying 'move over and up'?

Write two or three sentences. Use the mathematical steps from the mission as evidence—not only the final answer.

Take the mission offline

Workbook and teaching support

Continue on paper, teach it in class, or send the guided activity home.

STUDENT PDF

Mission Workbook

Foundation notes, guided practice, final scenario and reflection.

Download workbook ↓TEACHER / PARENT PDF

Teaching Guide

Lesson flow, support prompts, misconceptions and complete answers.

Download guide ↓
Senior 2 SHOWCASE MISSION

You made the mathematics visible.

A strong answer does not guess. It represents, calculates and explains.

Choose another room →