Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to turn coordinate differences into a distance.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Signed subtraction and the Pythagorean theorem.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Find the distance between A(−2, 1) and B(4, 9) in a coordinate plane with equal axis units.
Why this math matters
The straight-line distance between two points is the hypotenuse formed by their horizontal and vertical differences. Separate direct distance from a route constrained to horizontal and vertical streets.
Set up the model
A useful answer starts with clear assumptions:
- Both axes use the same length unit and scale.
- The desired distance is the straight segment between the points.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Turn coordinate differences into a distance
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find the distance between A(−2, 1) and B(4, 9) in a coordinate plane with equal axis units.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
horizontal change = 4 − (−2) = 6; vertical change = 9 − 1 = 8
Coordinate differences create the legs of an axis-aligned right triangle.
Apply the relationship
distance² = 6² + 8² = 100
The diagonal segment is the hypotenuse.
Check and interpret
distance = √100 = 10 units
The positive root gives a nonnegative geometric distance.
The result
distance = √100 = 10 units
The positive root gives a nonnegative geometric distance.
Common mistakes to catch
- Adding absolute coordinate differences gives a grid-route distance, not generally the straight-line distance.
- The standard formula presumes matching length units on the two axes.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Find the distance from (1,2) to (4,6).
Show a hint
Use changes of 3 and 4.
Reveal answer and explanation
5 units
√(3² + 4²) = √25 = 5.
Practice 2
What is the distance between (−3,7) and (−3,−2)?
Show a hint
The horizontal change is zero.
Reveal answer and explanation
9 units
The points lie vertically above one another, so distance is the magnitude of −2 − 7.
Take the idea with you
Separate direct distance from a route constrained to horizontal and vertical streets.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
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