THE COMPOUND // FIELD NOTES // WEEK 24
Distance formula and systems in three variables
Field Book
Lessons 88 to 91
Due
Test 21 due · Supplement 24
Method
Paper first, every step
Escape 6 posts this week. Lesson 90 comes with furniture instructions: turn the paper sideways and rule five columns before you touch a 3 by 3 system.
What you have to be able to do
- Compute distance between two points
- Read conjunctions and disjunctions, and use chord and secant products
- Solve three equations in three variables by organized elimination
The procedures
The distance formulaField Book Lesson 88
- D = √((x2 - x1)2 + (y2 - y1)2): the Pythagorean theorem in coordinates.
- PV = nRT problems continue as abstract equation practice.
Conjunctions and disjunctionsField Book Lesson 89
- A conjunction demands both conditions: the overlap. A disjunction accepts either: the union.
- Crossing chords: the products of the two segments of each chord are equal.
Three by three systemsField Book Lesson 90
- Turn the paper sideways and rule five columns to keep the work honest.
- Eliminate one variable from two different pairs, then solve the 2 by 2 that remains.
Linear inequalitiesField Book Lesson 91
- Four types: greater, greater or equal, less, less or equal.
- Graph the boundary line, dash it for strict, and shade the true side.
Worked: distance
- Find the distance from (0, 0) to (3, 4).
- D = √(32 + 42) = √25.
- D = 5.
Terms on the record
| Term | Meaning |
|---|
| distance formula | the Pythagorean theorem applied to coordinates |
| conjunction | a compound condition true only when both parts hold |
| disjunction | a compound condition true when either part holds |