9514 1404 393
Answer:
(c) (-6, 1)
Explanation:
The answer choices suggest the missing point is in the 2nd quadrant and below the given point in that quadrant. (All the x-values are negative, and the y-values are less than 6.)
There are at least a couple of ways you can find this point. We choose to consider the points of the opposite side: the two points in the first quadrant.
The bottom of these is 2 units left of the top one, and 5 units below it. (You can determine this by counting grid squares or by comparing coordinates.)
So, a point 2 left and 5 below the upper left point (-4, 6) will have coordinates ...
(-4, 6) +(-2, -5) = (-4-2, 6-5) = (-6, 1) . . . . the missing point
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Alternative solution
The midpoints of the diagonals of a parallelogram are the same point, so the sum of coordinates at the ends of each diagonal will be the same. This means you can find the missing point (D) using A+C-B = D, where A, B, C are the given points labeled clockwise from upper left.
D = A +C -B = (-4, 6) +(1, 2) -(3, 7) = (-4+1-3, 6+2-7)
D = (-6, 1)
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Additional comment
This relation between point coordinates is true regardless of how the given points are labeled. A different labeling will give a different point D, meaning 3 points can be the vertices of 3 different parallelograms. That is why we start this answer with a comment regarding where we expect the 4th point to be.