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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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