MEASURE · CHAPTER 1

MEASURE — Distance Parallel to the Axes

Think first. Use AI purposefully. Verify always.

01 · DISCOVER

Start with a question.

Two points share a row. Which coordinate can change as you travel from one to the other?

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

02 · UNDERSTAND

Distance Parallel to the Axes

A horizontal segment keeps y fixed; a vertical segment keeps x fixed. Count equal grid intervals, including intervals across zero. Reversing your journey changes the sign of the subtraction, but not the distance.

03 · KEY IDEAS

Key Ideas

Same y? Compare x. Same x? Compare y.
Horizontal distance: | $x_{2}$ − $x_{1}$ |. Vertical distance: | $y_{2}$ − $y_{1}$ |.
Absolute value gives the non-negative size of a difference. Coincident points have distance zero.

04 · VISUALISE

Explore the idea.

One interval = one unit.

Explore, then verify

Point Ax: -3y: 2

Point Bx: 2y: 2

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

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.

05 · METHOD

From understanding to a method.

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

06 · ONE WORKED EXAMPLE

Follow each step.

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

Both y-coordinates are 2: the segment is horizontal.
From −3 to 0 is 3 units; from 0 to 2 is 2 units.
AB = |2 − (−3)| = 5 units. Reversing gives |−3 − 2| = 5.

One interval = one unit.

Read the matching diagram

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.

07 · AIMS METHOD

Your turn to reason.

Attempt independently
Investigate the idea
Make connections
Scrutinise your reasoning

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

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 · MEASURE

Now connect with your textbook.

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

Exercise Practice

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