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A (4,0).B (1.5), and C(-3,-5) are three vertices of a parallelogram ABCD. What is the ordered pair for D, the fourth vertex of the parallelogram?

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Answer: In a parallelogram, opposite sides are equal in length and parallel, so if we subtract the vectors AB and BC from each other, we will get the vector for CD.

Given A = (4,0), B = (1.5,0), and C = (-3,-5), we can calculate the vectors AB and BC as follows:

AB = B - A = (1.5, 0) - (4, 0) = (-2.5, 0)

BC = C - B = (-3, -5) - (1.5, 0) = (-4.5, -5)

Next, we subtract these vectors to find the vector for CD:

CD = BC - AB = (-4.5, -5) - (-2.5, 0) = (-2, -5)

Finally, we add the vector CD to vertex C to find vertex D:

D = C + CD = (-3, -5) + (-2, -5) = (-5, -10)

So, the ordered pair for vertex D is (-5, -10).

Explanation: