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- Find the missing endpoint when the midpoint and one endpoint are given:
- Find a midpoint and the length of a median of a triangle.
- Find the far end of a boardwalk on a park map from its start and the bird hide at the middle.
- Find the mistake in Diego's search for an endpoint.
- Use the midpoint to find k, then check with the other coordinate.
- Decide whether each line is the perpendicular bisector of a segment, and say which condition fails.
- Find the center and radius of a circle in the complex plane from the ends of a diameter.
- Reflect a point through a center twice and compare the result to a single move.
- Find all three possible fourth corners of a parallelogram.
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The free lesson teaches it with worked examples and practice problems.
The midpoint formula: the lesson ›More Chapter 1 worksheets: Points, lines, planes and the language of proof
- 1.1Axioms, definitions and theorems
- 1.2Points, lines and planes
- 1.3Lines and planes in space
- 1.4The midpoint formula
- 1.5Conjecture, and why a pattern is not a proof
- 1.6Counterexample
- 1.7Inductive reasoning
- 1.8Deductive reasoning
- 1.9Statements and negation
- 1.10Conditionals, converse, inverse, contrapositive
- 1.11Biconditional
- 1.12Converses and biconditional definitions