The cases where AB=AC (blue), AB=BC (red), and AC=BC (green) (lighter versions on the left side of the y-axis) are shown below for measures of angle C between 0 and 180°. Mangaldan's comment), and by symmetry this perpendicular bisector of AB also bisects $\angle ACB$ from there, you can use right triangle trigonometry to determine the coordinates of C (left for you to solve). In the third case, C is equidistant from A and B, so C must lie on the perpendicular bisector of AB (as in J. Triangle A B C has point A at negative four, negative six, point B at two, negative eight, and point C at negative six, negative two. The second case is similar to the first (so it's left for you to solve). Find the area, in square units, of A B C triangle ABC A B C triangle, A, B, C plotted below. Edit (to match revised question): Given your revised question, there is still the issue of C being on either side of the y-axis, but you have specified that AB=AC and that you are given $\mathrm\angle C))$. Learn how to classify triangles in the coordinate plane using the distance formula and the pythagorean relations.
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