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# SAT Coordinate Geometry

$$\ \$$
In the diagram above, $$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) $$\ \ 10t$$

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) $$\ \ 100$$

\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) $$\ \ 36$$

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) $$\ \ (18, 18)$$

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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