1 / 17

Algebra 2

Algebra 2. Chapter 9 Conic Sections: Circles and Parabolas. 9-1 Distance and Midpoint Formulas. WARMUP: Simplify: -5 + 2 5. ( -1 – (-4)) 2 | -2 + (-6) | (3 – (-5)) 2 – ( -4 - 2) 2. 9-1 Distance and Midpoint Formulas.

hosea
Download Presentation

Algebra 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Algebra 2 Chapter 9 Conic Sections: Circles and Parabolas

  2. 9-1 Distance and Midpoint Formulas • WARMUP: • Simplify: • -5 + 2 5. • ( -1 – (-4))2 • | -2 + (-6) | • (3 – (-5))2 – ( -4 - 2)2

  3. 9-1 Distance and Midpoint Formulas • Objective: To find the distance between any two points and the midpoint of the line segment joining them.

  4. 9-1 Distance and Midpoint Formulas • Chapter 9 has a subtitle of “Conic Sections”. • http://clem.mscd.edu/~talmanl/HTML/ConicSections.html

  5. 9-1 Distance and Midpoint Formulas • How do we tell the distance between any two points on a number line?

  6. 9-1 Distance and Midpoint Formulas • The distance between any two points P and Q is written PQ. On a number line, PQ is the absolute value of the difference between their coordinates. • Since | a – b | = | b – a | order doesn’t matter. • Example:

  7. 9-1 Distance and Midpoint Formulas • What about two points in a coordinate plane? • Pick two points…

  8. 9-1 Distance and Midpoint Formulas • Reminder: Pythagorean Theorem: If the length of the hypotenuse of a right triangle is c, and the lengths of the other two sides (legs) are a and b, then

  9. 9-1 Distance and Midpoint Formulas

  10. 9-1 Distance and Midpoint Formulas • The Distance Formula: The distance between the points and is:

  11. 9-1 Distance and Midpoint Formulas • Find the distance between: • points: ( -2, -1 ) and ( -4, 3 ) • points: ( 2, -7 ) and ( 2, -1 )

  12. 9-1 Distance and Midpoint Formulas • The distance formula can be used to prove the Midpoint Formula: • The Midpoint Formula: The midpoint (M) of the line segment joining and is

  13. 9-1 Distance and Midpoint Formulas • Find the midpoint of the line segment joining the points: • ( 4, -6 ) and ( -3, 2 ) • ( 7, 5 ) and ( -1, -3 )

  14. 9-1 Distance and Midpoint Formulas • Typical test question: • Find the coordinates of Q given that M is the midpoint of the line segment PQ: P( 0, 0 ), M( 3, 5 ) Can do it graphically. On a test you MUST do it mathematically…

  15. 9-1 Distance and Midpoint Formulas

  16. 9-1 Distance and Midpoint Formulas • More examples:

  17. 9-1 Distance and Midpoint Formulas • Homework:

More Related