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\(\ \ \)

In the diagram above, \(A=(6, t), B=(8, t), C=(8, 6t),\) and \(D=(6, 6t)\). If the area of rectangle \(ABCD\) is \(200\), which of the following is the value of \(t\)?

In the diagram above, \(A=(6, t), B=(8, t), C=(8, 6t),\) and \(D=(6, 6t)\). If the area of rectangle \(ABCD\) is \(200\), which of the following is the value of \(t\)?

(A) \(\ \ 1\)

(B) \(\ \ 2\)

(C) \(\ \ 20\)

(D) \(\ \ 5t\)

(E) \(\ \ 10t\)

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Which of the following is the area of a triangle with vertices \(A=(10, 5), B=(15, 5),\) and \(C=(17, 15)\)?

(A) \(\ \ 0\)

(B) \(\ \ 10\)

(C) \(\ \ 25\)

(D) \(\ \ 50\)

(E) \(\ \ 100\)

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\[\begin{align} &M(9, 12)\\ &N(11, 12)\\ &P(11, 7)\\ \end{align}\]

The coordinates of points \(M, N,\) and \(P\) form the triangle \(\triangle MNP\) in the \(xy\)-plane. What is the perimeter of \(\triangle MNP?\)

(A) \(\ \ 5\)

(B) \(\ \ 7\)

(C) \(\ \ 7+\sqrt{21}\)

(D) \(\ \ 7+\sqrt{29}\)

(E) \(\ \ 36\)

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If \(P=(3, 11)\) and \(Q=(3, 18)\) are two consecutive vertices of a rectangle, which of the following CANNOT be another of its vertices?

(A) \(\ \ (-18, 11)\)

(B) \(\ \ (-11, -11)\)

(C) \(\ \ (11,18)\)

(D) \(\ \ (18, 11)\)

(E) \(\ \ (18, 18)\)

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If \((2, 3)\) and \((10, 11)\) are the endpoints of a circle's diameter, what are the coordinates of its center?

(A) \(\ \ (-4, -4)\)

(B) \(\ \ (0, 0)\)

(C) \(\ \ (6, 7)\)

(D) \(\ \ (5, 21)\)

(E) \(\ \ (12, 14)\)

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