APPLY · CHAPTER 1

APPLY — Coordinate Geometry in Action

Think first. Use AI purposefully. Verify always.

01 · DISCOVER

Start with a question.

A quadrilateral looks like a rectangle on a sketch. What coordinate evidence could verify that claim?

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

02 · UNDERSTAND

Coordinate Geometry in Action

A picture suggests a relationship; coordinates let you test it. Choose only the tools the claim needs. Shared coordinates show horizontal or vertical sides, lengths compare segments, and midpoints locate centres.

03 · KEY IDEAS

Key Ideas

Plot → Observe → Measure → Connect → Verify.
Equal lengths alone do not prove every property of a shape.
For three distinct collinear points with B between A and C, AB + BC = AC.
A midpoint check needs both equal distances and membership of the segment.

04 · VISUALISE

Explore the idea.

One interval = one unit.

Explore, then verify

Point Ax: -2y: -1

Point Cx: 2y: 3

Drag a point, or focus a slider and use arrow keys.

A(-2, -1), B(2, -1), C $(2, 3)$ , D(-2, 3). Choose a property to verify.

The axis-aligned shape has width 4 and height 4. It is a square.

05 · METHOD

From understanding to a method.

State the claim, plot the data with a uniform scale, choose a relevant calculation, and explain what that calculation proves.

06 · ONE WORKED EXAMPLE

Follow each step.

A $(- 2, - 1)$ , B $(2, - 1)$ , C $(2, 3)$ , D $(- 2, 3)$ mark a layout. Verify its shape and centre.

AB and CD are horizontal; BC and DA are vertical. Adjacent sides meet at right angles.
All four side lengths are 4. The layout is a square (and therefore also a rectangle).
Both diagonal midpoints are $(0, 1)$ . Each diagonal has length $\sqrt{32}$ . These checks agree with the plotted shape.

One interval = one unit.

Read the matching diagram

A(-2, -1), B(2, -1), C $(2, 3)$ , D(-2, 3). Choose a property to verify.

The axis-aligned shape has width 4 and height 4. It is a square.

07 · AIMS METHOD

Your turn to reason.

Attempt independently
Investigate the idea
Make connections
Scrutinise your reasoning

A $(0, 0)$ , B $(1, 1)$ , and C $(2, 0)$ satisfy AB = BC. Is B the midpoint of AC? Explain.

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 · APPLY

Now connect with your textbook.

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

Exercise Practice

End-of-Chapter Practice

Connections to other stages

Exercise Set 1.2 · Q4(i) →Also connects to NAVIGATE · solution kept in its primary location
End-of-Chapter ★ Q8 →Also connects to ORIENT · solution kept in its primary location
End-of-Chapter ★ Q11 →Also connects to HALFWAY · solution kept in its primary location
End-of-Chapter ★ Q12 →Also connects to CONNECT · solution kept in its primary location
End-of-Chapter ★ Q13 →Also connects to HALFWAY · solution kept in its primary location
End-of-Chapter Q14 →Also connects to NAVIGATE · solution kept in its primary location

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