Stitz-Zeager_College_Algebra_e-book

Related to nding the distance between two points is

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Unformatted text preview: y − 2)2 (y − 2)2 12 √ ± 12 √ ±2 3 √ 2±2 3 squaring both sides extracting the square root √ √ We obtain two answers: (1, 2 + 2 3) and (1, 2 − 2 3). The reader is encouraged to think about why there are two answers. Related to finding the distance between two points is the problem of finding the midpoint of the line segment connecting two points. Given two points, P (x1 , y1 ) and Q (x2 , y2 ), the midpoint, M , of P and Q is defined to be the point on the line segment connecting P and Q whose distance from P is equal to its distance from Q. Q (x2 , y2 ) M P (x1 , y1 ) If we think of reaching M by going ‘halfway over’ and ‘halfway up’ we get the following formula. Equation 1.2. The Midpoint Formula: The midpoint M of the line segment connecting P (x1 , y1 ) and Q (x2 , y2 ) is: M= x1 + x2 y1 + y2 , 2 2 If we let d denote the distance between P and Q, we leave it as an exercise to show that the distance between P and M is d/2 which is the same as the distance between M and Q. This suffices to show that Equation 1.2 gives the coordinat...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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