Waste less time on Facebook — follow Brilliant.
×

Functions

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

×

Problem Loading...

Note Loading...

Set Loading...