Geometry Problems
1. The vertices of rectangle ABCD are A = (0,0), B = (2a, 0), C = (2a, 2b), and D = (0, 2b). Where M, N, P, and Q are the midpoints of the consecutive sides of ABCD, what type of quadrilateral is MNPQ? Be as specific as possible.
2. Let p represent any positive number. Being as specific as possible, describe the type of triangle with vertices at (0,0), (p, 0), and (0, p).
3. Solve the following system of equations by graphing. -4x + 3y = 15 2x + y = -5
4. The graphs of the lines 3x + 4y = 2, 5x -y =11, and x + ky = -2 all contain the same point. Find the point and also the value of k.
5. Find the exact volume and exact lateral area of the solid formed when the region bounded by Quadrant I bye the lines x= 9, and y = 5 is revolved about the x-axis.
6. A circle has its center at the point (-2,3). If one endpoint of the diameter is at (3, -5), find the other endpoint.
7. There are two points on the x-axis at a distance of 6 units from the point (3,1). Determine the coordinates of each point.