SAT Math · Study & Practice
Coordinate Geometry
Coordinate geometry puts geometry on the xy-plane, where points have coordinates and lines have slopes. This chapter covers the distance and midpoint formulas, slope, and using coordinates to reason about parallel and perpendicular lines. Read each topic, work the problems with the hint ladder, then take the 8-question topic test.
Topics
1
Distance Formula
Start →
2
Midpoint Formula
Start →
3
Slope Applications
Start →
4
Coordinate Proofs
Start →
Chapter test
Formula Reference Sheet
This chapter
Two-point formulas
| Distance | √[(x₂ − x₁)² + (y₂ − y₁)²] |
|---|---|
| Midpoint | ((x₁ + x₂)/2, (y₁ + y₂)/2) |
| Slope | (y₂ − y₁)/(x₂ − x₁) |
Line relationships
| Parallel lines | equal slopes |
|---|---|
| Perpendicular lines | slopes are negative reciprocals |
| Horizontal / vertical | slope 0 / undefined |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
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