An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(4 ,9 )# to #(1 ,0 )# and the triangle's area is #32 #, what are the possible coordinates of the triangle's third corner?

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Answer 1 · 2018-01-08T09:03:31

Coordinates of #A = (0.6642, 2.3667)#

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#a = sqrt((4-1)^2 + (9-0)^2) = 9.4868#

#A_t = (1/2) a h #

#h = (2 * 32) / 9.4868 = 6.7462#

#tan theta = m = h / (a/2) = (2*6.7462) / 9.4868 = 1.4222#

Equation of line passing through B and slope m is

#y - 9 = 1.4222 (x - 4)#

#y - 1.4222 x = 3.3112# Eqn (1)

Equation of line passing through C and slope (-m) is

#y - 0 = -1.4222(x - 1)#

#y + 1.4222x = 1.4222# Eqn (2)

Solving Eqns (1), (2) we get the coordinates of point A.

#x = 0.6642 , y = 2.3667#