CHAPTER 1 · RESOURCES

MEASURE — 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

Distance Parallel to the Axes

Same y? Compare x. Same x? Compare y.
Horizontal distance: |x₂ − x₁|. Vertical distance: |y₂ − y₁|.
Absolute value gives the non-negative size of a difference. Coincident points have distance zero.

Check the shared coordinate. Subtract the other coordinates, then take the absolute value. State the distance in units.

One interval = one unit.

A(-3, 2), B $(2, 2)$ . Horizontal change 5; vertical change 0. AB = 5 units.

Signed change may be negative. Distance is never negative.
Same y → compare x.
Signed change = 5; distance = 5 units.

Find the distance from A(−3, 2) to B(2, 2).

AB = |2 − (−3)| = 5 units. Reversing gives |−3 − 2| = 5.

A signed change can be negative; a distance cannot.

A learner says the distance from (2, 4) to (2, −1) is −5. What needs correcting?

Check your reasoning

The vertical change is −5, but the distance is |−5| = 5 units.