# A rectangle has three of its vertices at points #(3,4), # #(5,–4),# and #(–7, –7).# What is the #y# coordinate of the unknown vertex?

The

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The vertices are labelled

Solving,

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To find the y-coordinate of the unknown vertex of the rectangle, we first need to determine the length of one of its sides. We can do this by calculating the distance between two known vertices. Let's choose the vertices (3,4) and (5,-4).

Using the distance formula, the distance between these two points is:

[ \sqrt{((5-3)^2 + (-4-4)^2)} = \sqrt{4^2 + 8^2} = \sqrt{16 + 64} = \sqrt{80} ]

Since a rectangle has equal opposite sides, this distance represents the length of one side of the rectangle.

Now, let's find the vector between the two known vertices: (3,4) and (5,-4). This vector will give us the direction from one point to the other.

[ \text{Vector} = (5-3, -4-4) = (2, -8) ]

To find the unknown vertex, we add this vector to one of the known vertices. Let's add it to the vertex (3,4):

[ \text{Unknown Vertex} = (3,4) + (2, -8) = (3+2, 4-8) = (5, -4) ]

So, the y-coordinate of the unknown vertex is -4.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- Two rhombuses have sides with lengths of #11 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?

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