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# TIU CET Review Math Session 4 Coordinate Geometry

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College Entrance Test Review …

College Entrance Test Review
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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### Transcript

• 1. COORDINATE GEOMETRY TIU Session 4 College Entrance Test Review
• 2. Rene Descartes
• Father of Modern Philosophy
• Many contributions to math:
• Cartesian Coordinate System
• Which uses ALGEBRA to describe GEOMETRY
• Descartes’ Rule of Signs
• 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
• SLOPE
• MIDPOINT
• LENGTH OF A LINE SEGMENT (or DISTANCE BETWEEN TWO POINTS)
• 6. SLOPE OF A LINE / LINE SEGMENT
• Steepness
• 7. SLOPE – usually computed using two given points
• Given the points
• P(7, 2) and Q (3, -5)
• in a plane. Find the slope of the line containing these two points.
• the slope m of line
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
• Midpoint M of two points P and Q
• Given the points P(7, 2) and Q(3,-5) in a plane. Find the midpoint of these two points.
• 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