Download Solving Quadratic Equations by Completing the Square

10.1
Introduction to Analytic
Geometry
Objective:
Find the distance and midpoint between two points on a
coordinate plane.
Prove geometric relationships among points and lines
using analytical methods.
How can you find the distance between point A and point B?
Pythagoras to the rescue!
a2 + b2 = c2
B
6
A
12
Distance Formula
The distance formula is very simply derived
from the Pythagorean Theorem.
a2 + b2 = c2
𝑑=
c2 = a2 + b2
𝑥2 − 𝑥1
2
𝑐=
+ 𝑦2 − 𝑦1
𝑎2 + 𝑏2
2
If we add an origin to our coordinate plane…
(4, 5) B
6
(0, 0)
A (-8, -1)
𝑑=
𝑥2 − 𝑥1
12
2
+ 𝑦2 − 𝑦1
2
Midpoint Formula
𝑥1 + 𝑥2 𝑦1 + 𝑦2
,
2
2
Average of the x’s.
Average of the y’s.
Determine whether quadrilateral ABCD with
vertices A(1, 1), B (0, -1), C(-2, 0), and D(-1, 2)
is a parallelogram.
Assignment
10.1 Practice Worksheet #1-8, 11