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{2|Two} : {1|One}, {or|or even} \ {=|Equals} {2|Two}. {By the|Through the} corollary, {D|Deb} {is|is actually} [i(x2 + X3), | (2/3 + 2/3){]|}. {To find|To locate} {P|G}, {apply|utilize} ({III|3}), {remembering|recalling} {that A|that the} {corresponds to|matches} (x^, y-^) {and|as well as} {D|Deb} {to|in order to} (x„ y„). {J|T} (^i.2/1) (x2,{yo|years old}) {This gives|This provides} {x|by} ^ Xi + 2-^(X2 + {X|By},) {1|One} + {2|Two} {=|Equals} H^l + X2 + X^), {_|} yi + -^■i{y.2 + Vs) 1 + 2 = 3(2/1 + yo + Vs)- ^ns. Hence the abscissa of the intersection of the medians of a triangle is the average of the abscissas of the vertices, and similarly for the ordinate. The symmetry of these answers is evidence that the particular median chosen is Immaterial, and the formulas therefore prove the fact of the intersection of the medians. The result just found admits of extension to any polygon, and, with formulas (IV), illustrates the fact that the cooi'dinates of centers of gravity are found by taking average values. CARTESIAN COORDINATES 23 PROBLEMS 1. Find the coordinates of the middle point of the line joining (4, — 6) and (- 2, - 4). Ans. (1, - 5). 2. Find the coordinates of the middle point of the line joining (a + b, c + d) and (a — b,
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