Precalculus Day #3 Mr. Ueland 1 st Period Rm 162

Today in Precalculus Prayer Correct Assignment #1 “New” material: The Cartesian Coordinate System

Reminder on HW grading HOMEWORK (45%) – Assignments are a key part of this course. I expect every student to attempt to solve every problem I assign. To be scored, each paper must be legible and properly headed. Assignments will be scored on a 5 point basis as follows (assumes ALL are attempted): – % correct5 pts – 60-79% correct4 pts – 40-69% correct3 pts – 0-39% correct2 pts – Less than 19% correct1 pt

Review Which algebraic property? a) b) c) [commutative] [distributive] [nonsense]

P.2: Cartesian Coordinate System A two-dimensional system of uniquely representing points in a plane by ordered pairs, ex. (2, –3) First published by Rene Descartes (as Cartesius) in 1637 The coordinate axes are divided into 4 quadrants:

Absolute Value function The absolute value of a real number a is defined as: Example 2 a) | –4| = 4 Example 2 b) a Is negative

Properties of the Absolute Value function

The Distance Formula Finds the straight line distance between any two ordered pairs Relies on the Pythagorean Theorem Because of the presence of absolute values… coordinates may be entered in any order

The Distance Formula Q: How many equivalent distance formulas are there? A: Four

Example 3 Find the distance between the points (1,5) and (6,2) Give exact answers unless instructed otherwise

Example 3 Verify for yourself that the distance formula result is independent of which point you choose as pt 1 and which you choose as pt 2

The Midpoint Formula Finds the midpoint of any line with given endpoints (a,b) and (c,d) Because of the absence of any negative signs, coordinates may be entered in any order Just the “average” of the end points

The Equation of a circle Developed from the distance formula: [Standard form of a circle]

What is the equation of this circle?

Assignment 2 pp 19-22/1-11 odd, 17,21,25,27,41,45-51 odd Due tomorrow at the start of class