Coordinate Geometry Pathway

From First Points to a Perpendicular Puzzle

This workbook builds every skill you need — one small, clear step at a time — until you can solve a genuine SAT/precalculus-level construction problem involving ratios, slope, perpendicularity, and systems of equations.

10 prerequisite stages → 1 target problem (the exact problem shown at the top of the page) → 3 follow-up problems = 14 problems total, all on one scrolling page. Each one shows the concept and a fully worked example before you try it.
minutes
Top Edu Prep · SAT / IB / AP Math Pathway

Coordinate Geometry Pathway: From First Points to a Perpendicular Puzzle

Target Problem: In right triangle ABC (right angle at A), point D lies on CB with BD = 2·CD, point F lies on AB with CF = FB, and AD ⊥ CF at E. Given AC = 1, find AE.

How many steps does it take to get there? — 10 stages

  1. The coordinate plane
  2. Distance on a straight segment
  3. The Pythagorean theorem
  4. The distance formula
  5. Simplifying square roots
  6. Points equidistant from two points
  7. Dividing a segment in a ratio
  8. The slope of a line
  9. Perpendicular lines
  10. Solving a system of two lines
Then: 1 Target Problem + 3 Follow-Up Problems