College Algebra - DOC 2 by VII9jovw

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									                                       College Algebra
                                      Self-assessment B
                                    Mathematical Relations
Name: _____________________________________

Problem                                                   Answer
1. Name the ordinate of the ordered pair (-5, -7)         1.

2. In which quadrant is the point (3, -8) located>        2.

3. Give the range of the relation below                   3.
{(-2, 5 (-5, -4), (3, 0), (2, -1)}

4. Find the x – intercept of the relation 7x – 3y = -42   4.



5. Find the point symmetric to (7, 4) with respect to     5,
the y-axis

6. Find the point symmetric to (-2, -5) with respect to   6
the origin
                                                          .
7. Find the slope of the line 7x -2y = 31                 7.


8. Find the slope of a line perpendicular to              8.
the line 7x – 2y = 31

9. Given that the point (3, -5) belongs to the line       9.
7x – 2y = 31, find another friendly point. Use the
slope


10. Find the center of the circle                         10. center: ______
x  32  (y  7)2  49
11. Find the range of the circle                          11.
x  32          2
            (y  7)  49


12. Write the equation of a vertical line through the     12.
point (-2, 7)
13. Write the equation of the circle with radius 1 and    13
center at (-2, 0)


14. Find the midpoint of the line segment connecting      14.
the point (-8, 5) and (-4, -1)




15. Find an equation of the line with slope m = -3 and    15.
y-intercept b = 17.
Use the slope-intercept form of a line: y = mx + b


16. Find the slope m of the line through the points       16.
 (-3, 7) and (1, 4).




17. A vertical line has:                                  17.
a) 0 slope b) positive slope   c) negative slope
d) undefined slope

18. Use the point-slope form of a line:                    18.
y  y1  m( x  x1 ) to find the equation of the line that
contains the points (-3, 7) and (1, 4)
19. Write the equation of the transpose of the relation     19.
x  32  (y  7)2  49

20. Write the equation of the line that is symmetric to     20.
the line y = 7x +5 with respect to the y-axis




Problem 1: Consider the equation 5x + 4y = 31.
a) Does the point ( 3, 4) belongs to the line? Yes or no?         a) ______________



b) Find the slope of the line.                                    b) m = ______


c) Find three points of the line                                  c) _____________




d) Draw the line in the Cartesian System provided below.

                                        y




                                   -1   1 2 3 4                          x




e) On the graph above, shade the graph of the inequality 5x +4y >31
Problem 2. A circle contains the points (2, -3), (9, 4) and
(-21, 20)
Replacing the x values and y values in the general form of a circle,
x 2  y 2  Dx  Ey  F  0 results in the following system:
 2D  3E  F  13

 9D  4E  F  97
  21D  20E  F  841

a)
Using the Row Reduced Echelon Form (rref in the TI calculator) to to solve the system
for D, E and F, we obtain
                       D = 12, E= -24, F = -109
b) Write the general form of the circle by replacing D, E, F by the values found in part a)

Answer: _____________________________________


c) Completing the square: (Fill in the blanks)
                                                         
x 2  y 2  12x  24y  109  0  x 2  12x  y 2  24y  ______
 x 2  12x  _____ y 2  24y  144  109  36  144
x  ___ 2  (y  12) 2  289
d) The radius of the circle is __________

e) The center of the circle is ____________

								
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