document.write( "Question 717966: Find 4 values for k so that (-1,2), (-10,5) and (-4,k) are the vertices of a right triangle. \n" ); document.write( "

Algebra.Com's Answer #440692 by josgarithmetic(39617) $\"\"$ $\"About$

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Starting with Distance Formula, First take the square of distance between each point.\r
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\n" ); document.write( "\n" ); document.write( "One variable assigning form can give like this:\r
\n" ); document.write( "\n" ); document.write( "D[1] (-1,2) to (-10,5), $\"D%5B1%5D%5E2=90\"$
\n" ); document.write( "D[2] (-1,2) to (-4,k), $\"D%5B2%5D%5E2=9%2B%282-k%29%5E2\"$
\n" ); document.write( "D[3] (-10,5) to (-4,k), $\"D%5B3%5D%5E2=36%2B%285-k%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Three equations using pythagorean theorem can be written for those distance squared expressions:\r
\n" ); document.write( "\n" ); document.write( " $\"D%5B1%5D%5E2=D%5B2%5D%5E2%2BD%5B3%5D%5E2\"$ ,
\n" ); document.write( "and
\n" ); document.write( " $\"D%5B2%5D%5E2=D%5B1%5D%5E2%2BD%5B3%5D%5E2\"$ ,
\n" ); document.write( "and
\n" ); document.write( " $\"D%5B3%5D%5E2=D%5B1%5D%5E2%2BD%5B2%5D%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Take the expressions for each and fill into the pythagorean theorem equations, and solve for k. I did not finish the solution beyond what I wrote and posted so far. \n" ); document.write( "

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