Module 4: Analytic Geometry, Engineering Economy and Depreciation

1. The segment from (-1, 4) to (2, -2) is extended two times is own length. Find the terminal point.
2. Find distance from the point (2,1) to the line 4x - 3y + 5 = 0.
3. Find the equation of the line through point (3,1) that is perpendicular to the line x + 5y + 5 = 0
4. What is the equation of the line that passes thru (4,0) and is parallel to the line x - y - 2 = 0.
5. Compute the area of a triangle whose vertices at (5, 1), (-3,1) and (1, 7).
6. (6, -1) and (-3, 7) are the coordinates of two corners of a triangle. What should be the ordinate of the third corner so that the centroid would be at the origin.
7. A and B are vertices of the base of an isosceles triangle ABC. A is at point (1,2) and B at (4, -1). Compute the abscissa of the vertex C with an ordinate of 4.
8. Referring to #7, compute also its area.
9. Referring to #7, compute its altitude from point C.
10. Find the equation of the line passing through (1, 4) and parallel to the line 3x - 4y = 6.
11. Find the angle between 3x + 4y = 0 to the line 5x - 2y = 3.
12. What is the radium of the circle x² - y² - 10x + 4y - 196 = 0
13. Referring to #12, find the also its area.
14. Find the equation of a circle with radius of 4 and center at (1, 2).
15. Find the location of the latus rectum of a parabola x² = 16y
16. Find the equation of the parabola with its vertex at the origin and focus is on the x-axis and the parabola passes through the point (3, 4)
17. Find the location of the focus of the parabola (x + 2)² = -16 (y - 3).
18. Find the length of the latus rectum of an ellipse x²/16 + y²/9 = 1
19. Find the length of the major-axis of an ellipse x²/16 + y²/9 = 1
20. Find the length of the directrix of an ellipse x²/16 + y²/9 = 1
21. The amount of P12,800 in 4 years at 5% compounded quarterly.
22. What is the interest rate, compounded monthly is equivalent to 10% effective interest?
23. What is the present worth of P27,000 due in 6 years if money is worth 13% compounded semi-annually?
24. The first cost of a machine is P1,800,000.00 with a salvage value of P330,000 at the end of 8 years. Find the book value at the end of 5 years. Using a) straight line method b) declining balanced method c) sinking fund method d) sum-of-year-digit method. Use r = 5%
25. The first of certain equipment is P3,000,000.00 with a freight cost of P200,000.00 and taxes and legal fee of P360,000.00. if the salvage value of the machine is P300,0000 with an expected life of 8 years. Find the total depreciation at the end of 5th year. Using a) a) straight line method b) declining balanced method c) sinking fund method d) sum-of-year-digit method. Use r = 5%