Chapter 2 – Coordinates and Geometry – Where Shapes Meet Symbols …There is a really really funny math joke on the next slide… … Wait for it… CAUTION… Mr. Baumgartner made it up (it may not be as funny to you as it was to me!)
Chapter 2 – Coordinates and Geometry – Where Shapes Meet Symbols So… the square walks into the prom and walks up to the triangle and says … “what’s the point?”… “what’s your sign”… “are you just plane happy to see me”… “what’s your angle…. “
2.3 Distance from the Origin and 2.4 The Equation of a Circle By the end of the period… I will be able to… Investigate how to find the length of a line segment from the origin to any point Investigate the equation of a circle
2.3 Distance from the Origin and 2.4 The Equation of a Circle Warmup… Take a piece of graph paper… Draw the positive quadrant of the coordinate plane How can you find the length of the line segment (distance) from the origin (0,0) to the point (7,9)?
2.4-Equations of Circles ~ with center (0,0) ~ Notice my choice of ‘design template’ for this one…
(x,y) (0,0) l = (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 l = (x 2 - 0) 2 + (y 2 - 0) 2 l = x 2 + y 2
(x,y) (0,0) l = (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 l = (x 2 - 0) 2 + (y 2 - 0) 2 l = x 2 + y 2
(x,y) (0,0) l = (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 l = (x 2 - 0) 2 + (y 2 - 0) 2 l = x 2 + y 2
(x,y) (0,0) l = (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 l = (x 2 - 0) 2 + (y 2 - 0) 2 l = x 2 + y 2
(x,y) (0,0) l = (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 l = (x 2 - 0) 2 + (y 2 - 0) 2 r = x 2 + y 2 l = x 2 + y 2 r 2 = x 2 + y 2 x 2 + y 2 = r 2 r r
Example 1: Find the equation of a circle, with center (0,0), that has a radius of 11. Don’t forget to square the radius!
x 2 + y 2 = r 2 Example 1: Find the equation of a circle, with center (0,0), that has a radius of 11. x 2 + y 2 = 11 2 x 2 + y 2 = 121 Don’t forget to square the radius!
x 2 + y 2 = 36 Example 2: x 2 + y 2 = r 2 r 2 = 36 What is the radius of a circle, with center (0,0), that has an equation of x 2 + y 2 = 36 ? compare to equation r = 6
Example 3: x 2 + y 2 = r 2 Write the equation of a circle, with center (0,0), passing through (-9,2). (-9) = r = r 2 85 = r 2 sub. in ‘x’ & ‘y’ values Solve for r 2 x 2 + y 2 = r 2 x 2 + y 2 = 85 sub. r 2 into equation
Homework… Page 155, #1-5