1. Advanced Math Extension: Analytic Geometry
6-1
Advanced Math Extension: Analytic Geometry
Summary of Methods Commonly Used in Coordinate Proofs:
To prove line segments equal, use the distance formula to show that they have the same length.
To prove non-vertical lines parallel, show that they have the same slope.
To prove lines perpendicular, show that the product of their slopes is 1.
To prove that two line segments bisect each other, use the midpoint formula to show that each segment has the same midpoint.
To show that lines are concurrent, show that their equations have a common solution.

2. Coordinate Geometry uses actual points.
Analytic Geometry uses variables; zero is the only acceptable number. You use definitions and formulas (midpoint, distance, and slope).
(0, 0) x y
(a, 0)
(0, b)
Right Triangle
Place a geometric figure in a convenient position on the coordinate plane (usually placing a vertex on the origin).
Scalene Triangle
(0, 0) x y
(b, c)
(a, 0)
(0, 0) x y
(a, b)
(2a, 0)
Isosceles Triangle
(a, 0) x y
(0, b)
(a, 0)
Isosceles Triangle

3. Analytic Proofs
Place a geometric figure in a convenient position on the coordinate plane (usually placing a vertex on the origin).
(0, 0) x y
(0, 0) x y
Parallelogram
Rectangle using midpoints
(b, c)
(a+b, c)
(0, 2b)
(2a, 2b)
(a, 0)
(2a, 0)
(0, 0) x y
(0, 0) x y
Square
Rectangle w/out midpoints
(0, a)
(0, b)
(a, a)
(a, b)
(a, 0)
(a, 0)

4. Trapezoid using midpoints
Isosceles Trapezoid
Trapezoid using midpoints
(0, 0) x y y
(-b, c)
(b, c) Q R
(2b, 2c)
(2d, 2c) P S
(2a, 0)
(-a, 0)
(a, 0) x

5. Trapezoid Midsegment Theoremy
The midsegment of a trapezoid is parallel to the bases
The length of the midsegment of a trapezoid is half the sum of the lengths of the bases.
PROVE IT!
(2b, 2c)
(2d, 2c) x
(0, 0)
(2a, 0)

6. Analytic Proofs
A3-Block B1
#6* Marissa Hayley #8
ChristianA JB
#9 JoshC Sliker #1
Allie
Sasha #2
Max #3
Jennie #4
Kevin
Mikayla #5
Eric #6
Dena
Rachel #7
Courtney
Sarah #8
Michael
Patrick #9
Chris
Abby #1
Carolyn Gabby
#2/3
ChristianP David
#4 Jess Kayleigh
#5*
Alek Nathaniel
JoshS Zoe
#6*
Tyler John

7. Analytic Proofs
E-Block B4
#6*
Nate Mallorie #8
Boo Kasey #9
Ben K Austin #1
Sam G
Bobby
#2/3
Kara
Alicia #4
Abby
Aleah
#5*
Deanna
Kasi
*Ask for hint on placement
#6*
Evan
Alex #8
Jess
Floriana #9
Annalee
Sam T. #1
Kim Ben T.
#2/3
Conner Connor #4
Richard Anna
#5*
Alan David #5*
Rachel Natalie
#6*
Kevin Jack