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Math Session 4 Coordinate Geometry

Formulas for the Slope of a line, Midpoint, Distance between any two points,

Equations of a Line

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- 1. COORDINATE GEOMETRY TIU Session 4 College Entrance Test Review
- 2. Rene Descartes <ul><li>Father of Modern Philosophy </li></ul><ul><li>Many contributions to math: </li></ul><ul><ul><li>Cartesian Coordinate System </li></ul></ul><ul><ul><ul><li>Which uses ALGEBRA to describe GEOMETRY </li></ul></ul></ul><ul><ul><li>Descartes’ Rule of Signs </li></ul></ul>
- 3. Cartesian Coordinate System X-axis Y-axis Point – described as an ORDERED PAIR
- 4. Recall: Undefined terms in geometry? POINT – now described as (x, y) LINE – we will define as an equation: where x & y are unknowns, and a and b are known quantities. PLANE – the Cartesian plane (previous slide)
- 5. “ Features” of a LINE <ul><li>SLOPE </li></ul><ul><li>MIDPOINT </li></ul><ul><li>LENGTH OF A LINE SEGMENT (or DISTANCE BETWEEN TWO POINTS) </li></ul>
- 6. SLOPE OF A LINE / LINE SEGMENT <ul><li>Steepness </li></ul>
- 7. SLOPE – usually computed using two given points <ul><li>Given the points </li></ul><ul><li>P(7, 2) and Q (3, -5) </li></ul><ul><li>in a plane. Find the slope of the line containing these two points. </li></ul><ul><li>the slope m of line </li></ul>is given by = .
- 8. Graph of: Line segment with endpoints (7, 2) and (3, -5). Plotted by www.wolframalpha.com.
- 9. MIDPOINT OF TWO POINTS <ul><li>Midpoint M of two points P and Q </li></ul><ul><li>Given the points P(7, 2) and Q(3,-5) in a plane. Find the midpoint of these two points. </li></ul>
- 10. Midpoint – is like getting the AVERAGE – is a POINT, so your answer must have two coordinates. – Get the average of the X coordinates, and the average of the Y coordinates Midpoint Formula:
- 11. Given the points P(7, 2) and Q(3,-5) in a plane. Find the midpoint of these two points.
- 12. Distance between Two Points (or the length of a line segment) Given the points P(7, 2) and Q(3,-5) in a plane. Find the distance between these two points.
- 13. How do we get the length of the hypotenuse of a right triangle? Pythagorean Theorem:
- 14. Distance between two points Distance Formula
- 15. PRACTICE TIME!
- 16. EQUATIONS OF A LINE

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