Mark M. answered • 05/13/18

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Mathematics Teacher - NCLB Highly Qualified

Using slopes of perpendicular lines.

m

_{AC}= (k + 1 - 5) / (k + 2) ⇒ m_{AC}= (k - 4) / (k + 2)m

_{BC}= (k + 1 + 6) / (k - 8) ⇒ m_{BC}= (k + 7) / (k - 8)To be perpendicular

m

_{AC}= -1 / m_{BC}(k - 4) / (k + 2) = -(k - 8) / (k + 7)

(k - 4)(k + 7) = -1(k - 8)(k + 2)

k

^{2}+ 3k - 28 = -(k^{2}- 6k - 16)k

^{2}+ 3k - 28 = -k^{2}+ 6k + 162k

^{2}- 3k - 48 = 0Unless the arithmetic is in error (a possibility) the roots are irrational.

Arthur D.

^{2}-3k-44=0 which factors into (2k-11)(k+4)=005/13/18