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Unit 2 · 4 lessons

Analytic Geometry

Use coordinates to measure and prove: find the midpoint and length of a line segment, write the equation of a circle centred at the origin, build perpendicular bisectors, find the shortest distance from a point to a line, and verify properties of triangles and quadrilaterals with algebra.

  • 43 practice questions
  • 33 flashcards
  • 2 interactive lessons
Start lesson 1 →Unit 2 test review →

Lessons

  1. 1Midpoint and Length of a Line SegmentTwo formulas that turn coordinates into geometry: the midpoint formula averages the endpoints, and the length formula is the Pythagorean theorem written with coordinates. Learn where each one comes from, use both, and work backwards from a midpoint to a missing endpoint.Interactive11 questions
  2. 2Equation of a CircleEvery point on a circle is the same distance from the centre. Apply the length formula to that fact and you get the equation x² + y² = r² for a circle centred at the origin. Learn to read the radius from the equation, write the equation from the radius or a point, sketch the circle, and tell whether a point is inside, on or outside it.11 questions
  3. 3Slopes, Perpendicular Bisectors and Distance to a LineParallel lines share a slope and perpendicular lines have negative reciprocal slopes. Use those facts with the midpoint and length formulas to write the equation of a perpendicular bisector, and to find the shortest distance from a point to a line.11 questions
  4. 4Verifying Properties of Triangles and QuadrilateralsSlopes, lengths and midpoints turn "it looks like a rectangle" into a proof. Classify triangles and quadrilaterals from their vertices, verify the midsegment theorem and the diagonal properties of parallelograms and rectangles, work with medians, and plan a multi-step verification.Interactive10 questions