Parallelogram abcd has vertices: a(-3, 1), b(3, 3), c(4, 0), and d(-2, -2). in two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram abcd is a rectangle.

Step-by-step explanation:

Remember, the slope of parallel lines is the same, while the slope of perpendicular lines is the negative reciprocal of each other.

We are given that points a(-3,1), b(3,3), c(4,0) and d(-2,-2). Let’s first identify the relationships between the lines that form the sides of rectangle ABCD.

Lines AD and BC are parallel

Lines AB and DC are parallel

Lines AB and AD are perpendicular

Lines BC and DC are perpendicular

Lines AD and BC are parallel, since the two lines share a slope of -3.

Lines AB and DC are parallel, since they both share a slope of 1/3.

Lines CD and BC are perpendicular, since they are the opposite reciprocal of each other. CD has a slope of 1/3. BC has a slope of -3.

Lines DC and AD are perpendicular as well. DC has a slope of 1/3. AD has a slope of -3.

Using this information, we can arrive at the conclusion that parallel lines DC and AB intersect with parallel lines BC and AD. The intersection of these pairs of parallel lines make up the sides of rectangle ABCD, which proves that the vertices of the parallelogram forms a rectangle.

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