MathematicsChapter 6: Analytical Geometry
Coordinate Distance and Midpoint
Distance follows Pythagoras; midpoint averages corresponding coordinates.
Learning objectives
- State the rule for coordinate distance and midpoint.
- Solve a coordinate distance and midpoint problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Distance follows Pythagoras; midpoint averages corresponding coordinates.
Formula
distance=4sqrt2 and midpoint
Where / symbols
- Coordinate distance and midpoint
- Distance follows Pythagoras; midpoint averages corresponding coordinates.
CONCEPT AND RULE
Distance follows Pythagoras; midpoint averages corresponding coordinates.
METHOD
For coordinate distance and midpoint, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
For A(1,2), B(5,-2), distance=4sqrt2 and midpoint=(3,0).
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve coordinate distance and midpoint
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Worked example
- Worked example:
- For A(1,2), B(5,-2), distance=4sqrt2 and midpoint=(3,0).
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Coordinate distance and midpoint
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Coordinate Distance and Midpoint
Sticky Notes · Formula and Worked Revision
Core Idea
- Distance follows Pythagoras; midpoint averages corresponding coordinates.
Rule / Formula
- Distance follows Pythagoras; midpoint averages corresponding coordinates.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- For A(1,2), B(5,-2), distance=4sqrt2 and midpoint=(3,0).
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Distance follows Pythagoras; midpoint averages corresponding coordinates.
- Worked pattern: For A(1,2), B(5,-2), distance=4sqrt2 and midpoint=(3,0).
- Final check: domain, sign, notation, units, and reasonableness.
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