College Algebra 9th txtbk

Review Exercises 159
8. Let M be the midpoint of A and B, where A (a 1 , a 2 ),
B (2, 5), and M (4, 3).
(A) Use the fact that 4 is the average of a 1 and 2 to find a 1 .
(B) Use the fact that 3 is the average of a 2 and 5 to find a 2 .
(C) Find d(A, M ) and d(M, B).
9. (A) Graph the triangle with vertices A (1, 2), B (4, 3),
and C (1, 4).
(B) Find the perimeter to two decimal places.
(C) Use the Pythagorean theorem to determine if the triangle is
a right triangle.
(D) Find the midpoint of each side of the triangle.
10. Use the graph of the linear function in the figure to find the rise,
run, and slope. Write the equation of the line in the form
Ax By C, where A, B, and C are integers with A 0. (The
horizontal and vertical line segments have integer lengths.)
11. Graph 3x 2y 9 and indicate its slope.
12. Write an equation of a line with x intercept 6 and y intercept 4.
Write the final answer in the standard form Ax By C, where
A, B, and C are integers.
13. Write the slope–intercept form of the equation of the line with
slope and y intercept 2.
2 3
5
5
5
14. Write the equations of the vertical and horizontal lines passing
through the point (3, 4). What is the slope of each?
y
5
x
21. Write the slope–intercept form of the equation of the line that
passes through the point (2, 1) and is
(A) parallel to the line 6x 3y 5
(B) perpendicular to the line 6x 3y 5
22. Find the equation of a circle that passes through the point (1, 4)
with center at (3, 0).
23. Find the center and radius of the circle given by
x 2 y 2 4x 6y 3
24. Find the equation of the set of points equidistant from (3, 3) and
(6, 0).What is the name of the geometric figure formed by this set?
25. Are the graphs of mx y b and x my b parallel, perpendicular,
or neither? Justify your answer.
26. Use completing the square to find the center and radius of the
circle with equation:
x 2 4x y 2 2y 3 0
27. Refer to Problem 26. Find the equation of the line tangent to the
circle at the point (4, 3). Graph the circle and the line on the same
coordinate system.
28. Find the equation of a circle with center (4, 3) whose graph
passes through the point (1, 2).
29. Extend the following graph to one that exhibits the indicated
symmetry:
(A) x axis only (B) y axis only
(C) origin only (D) x axis, y axis, and origin
5
5
y
5
x
Test each equation in Problems 15–18 for symmetry with respect to
the x axis, y axis, and the origin. Sketch the graph of the equation.
15. y x 2 2 16. y 2 x 2
17. 9y 2 4x 2 36 18. 9y 2 4x 2 36
19. Write a verbal description of the graph shown in the figure
and then write an equation that would produce the graph.
5
5
5
20. (A) Find an equation of the line through P (4, 3) and
Q (0, 3). Write the final answer in the standard form
Ax By C, where A, B, and C are integers with A 0.
(B) Find d(P, Q).
y
5
x
Problems 30 and 31 refer to a triangle with base b and height h
(see the figure). Write a mathematical expression in terms of b and
h for each of the verbal statements in Problems 30 and 31.
30. The base is five times the height.
31. The height is one-fourth of the base.
APPLICATIONS
h
5
b
32. LINEAR DEPRECIATION A computer system was purchased by a
small company for $12,000 and is assumed to have a depreciated
value of $2,000 after 8 years. If the value is depreciated linearly from
$12,000 to $2,000:
(A) Find the linear equation that relates value V (in dollars) to time
t (in years).
(B) What would be the depreciated value of the system after 5 years?