Answer:
(3, 7)
Explanation:
Given that points (-4,9), (-6,-5), and (1.-7) are three vertices of a parallelogram with segments connecting them in order, you want the point that is the fourth vertex.
Parallelogram
The diagonals of a parallelogram bisect each other, which means they have the same midpoint:
((-4, 9) +(1, -7))/2 = ((-6, -5) +(x, y))/2
Multiplying by 2 and subtracting the point on the right side, we have ...
(-4, 9) +(1, -7) -(-6, -5) = (x, y)
(-4 +1 +6, 9 -7 +5) = (x, y) = (3, 7)
The fourth vertex is (3, 7).
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Additional comment
In general three points can define three possible parallelograms. Here, the segments connecting the points are presumed to be the sides of the parallelogram, so reducing the number of possibilities to just one.
The fact that the diagonal midpoints are the same is useful for solving a variety of problems involving parallelograms.