Find the value(s) of y such that the triangle with the given vertices has an area of 8 square units. (Enter your answers as a comma-separated list.)
A(−4,5), B(−3,4), C(−1,y).
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A B C A
-4 -3 -1 -4
5 4 y 5
Add the diagonal products starting at the upper left.
-4*4 + -3y -1*5 = -3y - 21
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Add the diagonal products starting at the lower left.
5*-3 + 4*-1 - 4y = -4y - 19
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The ABS of the difference is y - 2
The area is 1/2 that = y/2 - 1
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y/2 - 1 = 8
y = 18
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The other difference is -y + 2
-y/2 + 1 = 8
y = -14