Precalc0011to0016-page17

Precalc0011to0016-page17 - of the x-coordinates of the...

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(Section 0.13: The Cartesian Plane and Circles) 0.13.2 PART C: DISTANCE AND MIDPOINT FORMULAS Distance Formula The distance between points Px 1 , y 1 () and Qx 2 , y 2 () in the Cartesian plane is given by: d = x 2 ± x 1 () 2 + y 2 ± y 1 () 2 or, equivalently, x 1 ± x 2 () 2 + y 1 ± y 2 () 2 • This is proven using the Pythagorean Theorem , which we will discuss in Chapter 4 on trigonometry. Midpoint Formula The midpoint of PQ , the line segment with endpoints P and Q , is given by: x 1 + x 2 2 , y 1 + y 2 2 ± ² ³ ´ µ • Observe that the x -coordinate is the average
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Unformatted text preview: of the x-coordinates of the endpoints, and the y-coordinate is the average of the y-coordinates. For example, in the figure below, the distance between the points 2,1 ( ) and 3, 3 ( ) is: d = 3 2 ( ) ( ) 2 + 3 1 ( ) 2 = 29 . If the coordinate axes are scaled in (say) meters, then the distance is 29 meters. The midpoint M of the red line segment is: 2 + 3 2 , 1 + 3 2 = 1 2 , 2...
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