F Elect 3 (Analytic ) Take home Exam

This are the additional problems to the first 3 problems given during
our lecture. Solve all problems and submit your solutions on
November 22, 2010 during our lecture.

4. Show that the points (-1, -2), (5, 4) and (-3, 0) are vertices of
a right triangle and find its area.

5. The center of a circle is at (-3, -2) and its radius is 7 units.
Determine the length of of the chord which is bisected at (3, 1).

6. The segment from (-1, 4) to (2, -2) is extended three times its
own length. Determine the terminal point.

7. Show that the points (1, 4), (7, 0), (5, -3) and (-1, 1) are vertices
of a rectangle, and find the area.

8. The center of a circle is at (2, -5) and one point on the circle is
(-4, 2). Determine the other end of the diameter through (-4, 2).

9. The three vertices of a parallelogram are (1, -3), (-3, -1) and
     (3, 5). Determine the fourth vertex.

10. The segment joining (5, 11) and (-3, -1) is to be divided into four equal parts. Determine the points of division.