Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Pythagorean theorem wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
History of geometry wikipedia , lookup
Group action wikipedia , lookup
Tensors in curvilinear coordinates wikipedia , lookup
Multilateration wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
Rational trigonometry wikipedia , lookup
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 π= c2 = a2 + b2 π₯2 β π₯1 2 π= + π¦2 β π¦1 π2 + π2 2 If we add an origin to our coordinate planeβ¦ (4, 5) B 6 (0, 0) A (-8, -1) π= π₯2 β π₯1 12 2 + π¦2 β π¦1 2 Midpoint Formula π₯1 + π₯2 π¦1 + π¦2 , 2 2 Average of the xβs. Average of the yβs. 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