SOLUTION: Points A B C are three vertices of an isosceles triangle in which AC=BC . The coordinates of A and B are (-2,1) & (6,-3)respectively and the equation of AC is 4x-7y+15=0find the co
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-> SOLUTION: Points A B C are three vertices of an isosceles triangle in which AC=BC . The coordinates of A and B are (-2,1) & (6,-3)respectively and the equation of AC is 4x-7y+15=0find the co
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Question 1205117: Points A B C are three vertices of an isosceles triangle in which AC=BC . The coordinates of A and B are (-2,1) & (6,-3)respectively and the equation of AC is 4x-7y+15=0find the coordinates of C Answer by greenestamps(13203) (Show Source):
AC and BC are the congruent sides, so the third side is AB.
If M is the midpoint of AB, then MC is the altitude of the triangle.
The midpoint of AB is (2,-1).
The slope of AB is -1/2.
The slope of MC (the altitude to AB) is the negative reciprocal of the slope of AB: 2.
The equation of the altitude MC -- with slope 2 and passing through (2,-1) -- is y=2x-5.
I leave it to the student to fill in the details for the above calculations.
The intersection of MC and the given line is the point C whose coordinates we are to find. With the two equations in the form we have, solve using substitution:
