SOLUTION: Three points have coordinates A(1,2) to B(9,0) and C(6,t). Calculate the value(s) of t if: a) Angle ABC = 90 degrees, b) AC is perpendicular to BC.

Question 389008: Three points have coordinates A(1,2) to B(9,0) and C(6,t). Calculate the value(s) of t if:
a) Angle ABC = 90 degrees,
b) AC is perpendicular to BC.
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
a) ABC has a right angle in B if : BA.BC = 0 = (8,-2).(-3,t) = -24 - 2t = 0

2t = -24 => t = -12

b) AC = (5,t-2) BC = (-3, t) AC is perpendicular to BC is AC.BC = 0

AC.BC = -15 + t^2 - 2t = 0 = t^2 -2t - 15 = (t-5)(t+3)

hence t = -3 or 5
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