HALFWAY · CHAPTER 1

HALFWAY — Midpoint of a Line Segment

Think first. Use AI purposefully. Verify always.

01 · DISCOVER

Start with a question.

If you move halfway from A to B, what fraction of each coordinate change have you made?

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

02 · UNDERSTAND

Midpoint of a Line Segment

Halfway along a segment means half the horizontal change and half the vertical change. Starting from A and adding half each difference gives the average of each pair of corresponding coordinates.

03 · KEY IDEAS

Key Ideas

Average x-coordinates together and y-coordinates together.
The midpoint lies on the segment and is equally far from both endpoints.
Use the midpoint relationship and solve backwards: repeat the change from the known endpoint to the midpoint.

04 · VISUALISE

Explore the idea.

One interval = one unit.

Explore, then verify

Predict the midpoint of both coordinates before checking.

Point Ax: -2y: -1

Point Bx: 2y: 3

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

A(-2, -1), B $(2, 3)$ . Horizontal change 4; vertical change 4. AB ≈ 5.66 units.

05 · METHOD

From understanding to a method.

M (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

Add corresponding coordinates and halve each sum. Plot the result. Verify collinearity and equal endpoint distances.

06 · ONE WORKED EXAMPLE

Follow each step.

Find the midpoint of A $(- 2, - 1)$ and B $(2, 3)$ .

The average x-coordinate is (−2 + 2) ÷ 2 = 0.
The average y-coordinate is (−1 + 3) ÷ 2 = 1, so M $(0, 1)$ .
${AM}^{2}$ = $2^{2}$ + $2^{2}$ = 8 and ${MB}^{2}$ = $2^{2}$ + $2^{2}$ = 8. M lies on AB, so AM = MB = $\sqrt{8}$ .

One interval = one unit. M is the midpoint of AB.

Read the matching diagram

A(-2, -1), B $(2, 3)$ . Horizontal change 4; vertical change 4. AB ≈ 5.66 units. M $(0, 1)$ . AM = MB ≈ 2.83.

x: -2 → 0 → 2
y: -1 → 1 → 3
AM = MB. Half the change in each coordinate.

07 · AIMS METHOD

Your turn to reason.

Attempt independently
Investigate the idea
Make connections
Scrutinise your reasoning

A $(- 2, 1)$ and M $(1, 3)$ are an endpoint and midpoint. Find B.

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 · HALFWAY

Now connect with your textbook.

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

Exercise Practice

Exercise Set 1.2 · Q4(ii) →

★ AIMS Think+

AT+ · Explore deeper. Reason beyond the routine.

End-of-Chapter ★ Q9 →
End-of-Chapter ★ Q10 →
End-of-Chapter ★ Q11 →Also connects to APPLY
End-of-Chapter ★ Q13 →Also connects to APPLY

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