NAVIGATE · CHAPTER 1

NAVIGATE — Reading and Writing Coordinates

Think first. Use AI purposefully. Verify always.

01 · DISCOVER

Start with a question.

Would moving 3 units right then 1 unit up reach the same place as moving 1 unit right then 3 units up?

Make a prediction before exploring. You do not need a rule yet.

02 · UNDERSTAND

In an ordered pair, order carries meaning.

An ordered pair $(x, y)$ records horizontal position first and vertical position second. Each value is signed: its sign tells the direction from the origin. Swapping unequal values changes the point.

03 · KEY IDEAS

Key Ideas

x-coordinate: signed horizontal position from the origin.
y-coordinate: signed vertical position from the origin.
On the x-axis, y = 0. On the y-axis, x = 0.
The origin has coordinates $(0, 0)$ and lies on both axes.

04 · VISUALISE

Explore the idea.

One grid interval is one unit. Horizontal x first; vertical y second.

Read P from the graph

Trace the point to each axis. Say the horizontal value first, then the vertical value.

Make your own reading before checking.

05 · METHOD

Horizontal first. Vertical second.

To plot $(x, y)$ , start at O, move x units horizontally with its sign, then y units vertically with its sign. To read a point, trace to the axes and write x before y.

P = $(x, y)$

06 · ONE WORKED EXAMPLE

Follow each step.

Plot P $(- 2, 3)$ , then check it by reading back from the diagram.

The first coordinate is −2, so move 2 units left from O.
The second coordinate is 3, so move 3 units up.
Mark P at the crossing of x = −2 and y = 3.
Read back: horizontal −2, vertical 3. So P = $(- 2, 3)$ .

07 · AIMS METHOD

Your turn to reason.

Attempt independently
Investigate the idea
Make connections
Scrutinise your reasoning

A point is 4 units below the origin on the y-axis. What is its ordered pair?

Your reasoning

Your written reasoning is not automatically graded or sent anywhere.

08 · AIMS PRACTICE SPRINT

Vary the situation. Keep the idea.

Work through 10 questions on this concept. Select an answer before checking it; use the feedback to revise your reasoning.

Start practice sprint

09 · CHECK & FEEDBACK

Correct answers receive an explanation. Incorrect answers receive a hint and another attempt. This is practice, not an examination.

Review status is self-reported, not a mastery score. Progress is stored only in this browser; no account or tracking service is used.

TEXTBOOK CONNECTION · NAVIGATE

Now connect with your textbook.

Choose one item. Try it independently, then use an AIMS hint or compare the reasoning.

Exercise Practice

Exercise Set 1.1(ii) →
Exercise Set 1.2 · Q3(i) →
Exercise Set 1.2 · Q4(i) →Also connects to APPLY

End-of-Chapter Practice

End-of-Chapter Q14 →Also connects to APPLY

Original AIMS explanations linked to verified textbook references. Completion remains untracked.