CHAPTER 1 · RESOURCES
APPLY — Concept Note
Think first. Use AI purposefully. Verify always.
A concise revision of the approved lesson. For discovery, interaction and guided reasoning, return to the lesson.
CONCEPT
Coordinate Geometry in Action
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.
Formula / Property
State the claim, plot the data with a uniform scale, choose a relevant calculation, and explain what that calculation proves.
Visual / Diagram
One interval = one unit.
Read the matching diagram
A(-2, -1), B(2, -1), C, D(-2, 3). Choose a property to verify.
The axis-aligned shape has width 4 and height 4. It is a square.
Mini Example
A(−2, −1), B(2, −1), C(2, 3), D(−2, 3) mark a layout. Verify its shape and centre.
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 √32. These checks agree with the plotted shape.
Common Mistake
A sketch or equal lengths alone cannot justify every property of a shape. State what your calculation proves.
Quick Recall
A(0, 0), B(1, 1), and C(2, 0) satisfy AB = BC. Is B the midpoint of AC? Explain.
Check your reasoning
No. AB = BC = √2, but B is not on segment AC. The midpoint is (1, 0). A midpoint requires membership of the segment and equal distance from its endpoints.