Lecture #5 - 1.9.pdf - 1.9 Homework Due on MyMathLab by Monday June 11th by 10am 1.9 – Distance and Midpoint Formulas Circles For both formulas Let

# Lecture #5 - 1.9.pdf - 1.9 Homework Due on MyMathLab by...

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1.9 Homework Due on MyMathLab by Monday, June 11 th by 10am 1.9 – Distance and Midpoint Formulas; Circles For both formulas: Let the first point be represented as (x 1 , y 1 ) and the second point be represented as (x 2 , y 2 ). We use variables to represent the points in order to generalize the rules and formulas so that they can be used with most other numbers. Distance Formula o ࠵? = ( ࠵? ! ࠵? ! ) ! + ( ࠵? ! ࠵? ! ) ! o We use the distance formula to find the distance between any two points on the xy-coordinate plane. § Note: When I say “xy-coordinate plane”, this is the same coordinate plane that we have been using to graph. It has an x- axis, and a y-axis, therefore each point has an x-coordinate as well as a y-coordinate. “xy-coordinate plane” is just a more technical way of saying this. You can also say “coordinate plane” or “xy plane”. This is also referred to as a “Cartesian plane” or a “Cartesian coordinate system” (named after the man who invented this system). o After using the distance formula, remember to simplify the radical . Midpoint Formula o ( ! ! ! ! ! ! , ! ! ! ! ! ! ) o When you use the formula, what you end up getting out of it is a coordinate pair. § You are able to plot this coordinate pair as a point in the xy plane, but you won’t be asked to. o I’ve mentioned this before, but there is a rule in geometry that says between any two points, there is a line (or, a line can be formed between any two points). § Really, what a line is is a collection of points. The points are just so small that you can’t always see the all the points. § This is why when use a table of values to graph, we’re able to graph a few of the points and then form the line between them. o The purpose of the midpoint formula is to find the middle point between any two points in the xy-coordinate plane.

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• Spring '16
• Alexander rusinov

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