Triangle ABC has vertices A(3,1), B(5,7) and C(1, y). Find all y so that angle C is a right angle?

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Answer 1 · 2016-09-06T19:57:46

The two possible values of #y# are #3# and #5#.

For this problem, we need to consider AC be perpendicular to BC.

Since the lines are perpendicular, by the slope formula we have:

#(y_2 - y_1)/(x_2 - x_1) = -(x_2 - x_1)/(y_2 - y_1)#

#(y - 7)/(1 - 5) = -(1 - 3)/(y - 1)#

#(y - 7)(y - 1) = 2(-4)#

#y^2 - 7y - y + 7 = -8#

#y^2 - 8y + 15 = 0#

#(y - 3)(y - 5) = 0#

#y = 3 and 5#

Hopefully this helps!