10-1 The Distance and Midpoint Formulas

Ex 1a:Miss K and Batman are standing on a grid. They are specifically standing on the coordinate point (-2, 5). If their escape rout is a door at the origin, how could we find how far they must run to escape? Distance we want to find. 5 -2

The Distance Formula

Ex 1b: Big Bird, Mickey Mouse, and Yosemite Sam are all hanging out one day. Big Bird is at the point (2,0), Mickey Mouse is standing on the point (0,8), and Yosemite Sam is standing on the point (-2,0). What kind of triangle do these cartoon characters create? x y In order to know what kind of triangle it is, we need to know the lengths of the legs. DISTANCE FORMULA TO THE RESCUE!

Ex 1b: Big Bird, Mickey Mouse, and Yosemite Sam are all hanging out one day. Big Bird is at the point (2,0), Mickey Mouse is standing on the point (0,8), and Yosemite Sam is standing on the point (-2,0). What kind of triangle do these cartoon characters create? x y Note: we need to use the formula 3 to find the lengths of all 3 legs. From Big Bird (2,0) to Mickey Mouse (0,8):

Ex 1b: Big Bird, Mickey Mouse, and Yosemite Sam are all hanging out one day. Big Bird is at the point (2,0), Mickey Mouse is standing on the point (0,8), and Yosemite Sam is standing on the point (-2,0). What kind of triangle do these cartoon characters create? x y From Big Bird (2,0) to Yosemite Sam (-2,0)

Ex 1b: Big Bird, Mickey Mouse, and Yosemite Sam are all hanging out one day. Big Bird is at the point (2,0), Mickey Mouse is standing on the point (0,8), and Yosemite Sam is standing on the point (-2,0). What kind of triangle do these cartoon characters create? x y From Yosemite Sam (-2,0) to Mickey Mouse (0,8): Isosceles Triangle!

Ex 2: The Joker is trying to cut off Miss K and batman from reaching their escape rout. At what point would the joker cut them off at exactly the midpoint? Midpoint Formula: We want to find the midpoint between (-2,5) and (0,0):

Ex 2b: Write an equation to represent the perpendicular bisector between where Miss K is and where the escape is. The Perpendicular bisector consists of 2 things: -the midpoint -the perpendicular slope

Ex 2b: Write an equation to represent the perpendicular bisector between where Miss K is and where the escape is. The Perpendicular bisector consists of 2 things: -the midpoint -the perpendicular slope Plug them into the slope int. form:

Ex 2b: Write an equation to represent the perpendicular bisector between where Miss K is and where the escape is. The Perpendicular bisector consists of 2 things: -the midpoint -the perpendicular slope