# 1.9 - 1.9 Distance and Midpoint Formulas; Circles 1. Find...

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Unformatted text preview: 1.9 Distance and Midpoint Formulas; Circles 1. Find the distance between two points. The Distance Formula: The distance between two points R(XLY])al’ldP2(X2Y2), denoted by 0,0191%): (X2 _)(1)2 +(Y2 _Y1)2 XI 5! X2.— L12— Find the distance between (zﬁnﬁ) and (412%). ff’Tf—x C1: thL—m) +—(Hz~&)2' W : 6J2; aaﬁ V4. (as? «ﬂat; W :\J [esf¥>a ﬂ- [JEJa / _ q ('4) + 3 ’ 2. Find the midpoint of a line segment. The Miadmim Fart-win Consists? a iine segment whose endpoints are (xi. i 3%) and {3:3, 352}. The com-slip mates. of the segments midpoint are XI. + 1'1 3’1 “"3” F2 2 1 2 ' To find the midpoint, take the average of {its two moordinmes said the average of its: two git-coordinates. 2“ oh x2 ‘1?’ Find the midpoint of the line segment with and [—ipgj as endpoints. Y1 +X 2.— Lj 1+ [1 L Mic! Pom a l M) &. 5.2.3.. Vivi} \ )4 _JLgJL/y 3;ﬂ,%. L’/1 at 7, '34 €>3 3. Write the standard form of a circle’s equation. Beﬁtﬁtiun aft: Circle A circle is the 5%! m" all paints 51.1 a plane that are. equidistant tram a fixed mini, calicd tile emit-“trike fixed distance f'mm the Bimini; meter in an}? peim an the ﬁfth: is caiied {11:3 radius. “:11 Arty Witt? an the ﬁfth: ' {xx 3:}: The St'ﬁndafﬂ Farm (if 1:233 Equatigm fife! Circi-e The steward form (11‘ the equatian 0f :1 eireie With center {h k} and radian r is (.3: —— a}? + {3; -~— its)? r4”; The ﬂeueméﬁ Farm at” the Equatin {if a Circle The genemt ﬁrm {if the magniﬁer; {If a {’iféiﬂ is; \$2 .gn Ry: @ﬁx “r: 2,— where {A E; 2133:; F are we? numiwrﬁ. D. 2 ) (x—h + (a -I<) = V + 6,19) (5 4c) X-l—xk—kaz' 2 Xl—zxk—l—kL—Iegl—lﬂk’f'l‘ ’1 Y) Z 1—— )(L-t‘gj [email protected]< + 2+ k1»— \ . (Ha—r" "l (X—ln) -+ [3"K) :- k“ 4. Give the center and radius of a circle whose equation is in standard form. Write the standard form of the equation of the circle with center (-8, 5) and radiusJﬁ. ﬂ k K I“ a (X— (—eDZ—r— (ti-‘5) :iﬂ) % a—M 4592: H WW Xilwa—EL} +LjZ——IOH+Q5—z II at“ xl+ljl+lgxalog+ttﬁ : H 303% ﬁvan —105(+jr‘3’:—0 -. 41,36: 5. Convert the general form of a circle’s equation to standard form. Write the equation of the circle in standard form and give the center and radius. x2+y2—3x+5y—l=0 + 32+ “53 4E9;— 3 (if DH +%+§5 L’. #:131531— XZ+LJZ+<5’X ~33 —8 1‘— O Xz+<gx+ MD +71_;\j +__l__ 2%74—[644 ...
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## This note was uploaded on 01/16/2012 for the course MATH 126 taught by Professor Blisinhestiyas during the Fall '11 term at Truckee Meadows Community College.

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1.9 - 1.9 Distance and Midpoint Formulas; Circles 1. Find...

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