document.write( "Question 380119: The equilateral triangle is one in which all three sides are of equal length.\r
\n" ); document.write( "\n" ); document.write( "If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex. \n" ); document.write( "

Algebra.Com's Answer #269799 by robertb(5830) $\"\"$ $\"About$

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Note that the two vertices are located on the y-axis. Thus the y coordinate of the 3rd vertex must be midway between 0 and 4, i.e., y = 2. Hence the 3rd vertex is (x,2), where x is unknown.
\n" ); document.write( "Now the triangle with vertices (0,0), (0,2), and (x,2) is a 30-60-90 triangle, and so must have hypotenuse 4, shortest leg 2, and middle leg $\"2sqrt%283%29\"$ , by property of that triangle. The 3rd vertx is then( $\"2sqrt%283%29\"$ , 2).
\n" ); document.write( "Therefore there are two possible 3rd vertices: ( $\"2sqrt%283%29\"$ , 2), or ( $\"-2sqrt%283%29\"$ , 2)\r
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