Grade 10 Academic MPM 2 D Unit 2

Analytic Geometry The branch of mathematics that uses the x-y plane to determine equations

Distance to the Origin on a Plane The distance, d, from the origin (0,

Distance between two points on a Plane Given two points The distance d, is:

Midpoint between two points P & Q The midpoint is Average of x, Average

Example 1: Distance from the Origin on a Plane A pizza chain guarantees delivery

Example 1: Distance from the Origin on a Plane Continued a) For a pizza

Example 2: Distance between two points on a Plane Given the points: A (1,

Homework Work sheet: Distance on the Plane Text: • P. 151 #2, 3, 6

End of lesson Distance on the Plane © 2017 E. Choi – MPM 2

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Example 1: Distance from the Origin on a Plane A pizza chain guarantees delivery in 30 minutes or less. All orders are processed through a central office whose job, when an order is received, is to find the closest store in order to minimize the distance for its drivers. The company has set up a grid system, similar to the Cartesian plane, to locate its stores. The lines on the grid represent the major streets that run north-south and east-west. A(-8, 5) C(9, 5) B(9, -3) In the portion of the company’s grid map shown, the pizza chain has stores at locations and. If a pizza is to be delivered to a location in the grid at the origin (0, 0), which store should the central office call? The central office should call Store A. Distance on the Plane © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 1: Distance from the Origin on a Plane Continued a) For a pizza company, would the closest store always be the best choice for the central office? What other circumstances might the central office take into consideration? Traffic, available staffs, and how busy on certain location…. etc A(-8, 5) (0. 5, 5) C(9, 5) (0. 5, 1) (9, 1) B(9, -3) b) Find a point that would be the same distance from: i) stores A and B? ii) stores B and C? iii) stores A and C? Distance on the Plane © 2017 E. Choi – MPM 2 D - All Rights Reserved

Example 2: Distance between two points on a Plane Given the points: A (1, 2), B (6, 5) & C (5, -9) Find the distance between the following points a) AB b) AC c) BC Distance on the Plane © 2017 E. Choi – MPM 2 D - All Rights Reserved

Homework Work sheet: Distance on the Plane Text: • P. 151 #2, 3, 6 -11, 14 • P. 162 #2 a-f, 3, 4, 5, 8, 11 Check the website for updates Distance on the Plane © 2017 E. Choi – MPM 2 D - All Rights Reserved