document.write( "Question 1195474: Determine if the points (3,5), (3,3) and (2,4) are the vertices of a right triangle. Explain your rationale. \n" ); document.write( "

Algebra.Com's Answer #827975 by ikleyn(52867) $\"\"$ $\"About$

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\n" ); document.write( "Determine if the points (3,5), (3,3) and (2,4) are the vertices of a right triangle.
\n" ); document.write( "Explain your rationale.
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document.write( "Points A = (3,5) and B = (3,3) have the same x-coordinate.\r\n" );
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document.write( "It means that both points A and B lie on vertical line x= 3, parallel to y-axis.\r\n" );
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document.write( "Next,      points  A = (3,5) and C = (2,4)  have different y-coordinates; hence, line AC is not horizontal.\r\n" );
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document.write( "Similarly, points  B = (3,3) and C = (2,4)  have different y-coordinates; hence, line BC is not horizontal.\r\n" );
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document.write( "Thus, line AB is vertical, but angles A and B are not right angles.\r\n" );
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document.write( "So, we only should check if lines AC and BC are perpendicular.\r\n" );
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document.write( "Line AC has the slope   =  = 1.\r\n" );
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document.write( "Line BC has the slope   =  = -1.\r\n" );
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document.write( "Thus lines AC and BC are perpendicular, since their slopes are 1 and -1, i.e. negatively reciprocal \r\n" );
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document.write( "     (their product is  1 * (-1) = -1).\r\n" );
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document.write( "ANSWER.  Angle C is the right angle.\r\n" );
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