document.write( "Question 1200868: The vertices of triangle ABC are A(11,3), B(2k, k) and C(-1,-11).
\n" ); document.write( "(a) Find the two possible values of k if angle ABC is 90°.
\n" ); document.write( "(b) Draw the diagrams to show the two possible triangles \n" ); document.write( "

Algebra.Com's Answer #835110 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "For angle ABC to be 90 degrees, the segments AB and BC must be perpendicular, so the product of the slopes of the two segments must be negative reciprocals.

\n" ); document.write( "slope of AB: (2k-3)/(k-11)
\n" ); document.write( "slope of BC: (2k+11)/(k+1)

\n" ); document.write( " $\"%28%282k-3%29%2F%28k-11%29%29%28%282k%2B11%29%2F%28k%2B1%29%29=-1\"$

\n" ); document.write( " $\"4k%5E2%2B16k-33=-1%28k%5E2-10k-11%29\"$

\n" ); document.write( " $\"5k%5E2%2B6k-44=0\"$

\n" ); document.write( "The solutions are irrational; you can use the quadratic formula to find them.

\n" ); document.write( "The idea of the problem is good; however, it would have been far more educational if the solutions had been rational so a realistic diagram could be drawn.

\n" ); document.write( " \n" ); document.write( "

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