Let's assume these are the vertices in order and calculated the squared lengths of the sides. Let's calculate the vector for each side, which is the difference of the endpoints:
(7,10) - (4,7) = (3, 3)
(4,7) - (6,5) =(-2, 2)
(6,5) - (9,8) = (-3, -3)
(9,8) - (7,10) = (2, -2)
We see the pattern: (3,3) = -(-3,-3) and (-2,2) = -(2,-2)
We have two pairs of opposite vectors so we have a parallelogram.
Let's check the dot product of adjacent sides:
(3,3) . (-2, 2) = 3(-2) + 3(2) = 0
Zero dot product, we have perpendicularity. A parallelogram with one right angle is a
Answer: Rectangle
The adjacent sides are clearly not congruent so it's not a square
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