Name:
Period:
College Algebra: A.8 & A.9 and Ch.1.1, 1.4 & 1.5
A
You must show all your work for full credit. Ask me to clarify any questions you may have.
Question 0. If you could be any fictional (not real ) character, who would you choose? Explain (1 point)
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1. Use the points (-2, 5) and (4, -9) to answer the following questions.
a) Distance between the two points.
b) Midpoint of the segment containing the two points.
c) Equation of the line between the two points in slope-intercept form.
2. Find all points (x, y) with y-coordinate of 3 that are 113 units away from the point (4, -5).
3. If (-3, 5) is the endpoint of a line segment and (1, 3) is its midpoint, determine the other endpoint. Justify work.
4. Write an equation in standard and general form for the given circle with center (3, -2) and radius r = 5. Then graph
the circle.
5. Given the circle with equation 2 x 2  2 y 2  16 x  12 y  24  0 , find the following:
a) Find the center (h,k) and radius r of the circle.
b) Find any x-intercepts and y-intercepts of the circle. Express your answers as points.
6. Determine the standard form and general form of the equation of a circle with center (-2, 3) and that includes the
point (3, -1).
7. Determine the equation of the line perpendicular to 2 x  6 y  5 containing the point (2, -3) and give equation in
a) point-slope, b) slope-intercept, and c) general forms.
8. Find the equation of the line in slope-intercept form that connects the centers of the two given circles.
x 2  y 2  4x  4 y  1  0
and
x 2  y 2  6 x  12 y  3  0
Simplify and/or rationalize each expression.
9.
2 20
10.
3
11.
3
3
16
12.
80  20  12
2
23 5
52 5
13. True or False. Explain your reasoning.
a2  b2 = a + b
Solve each inequality. Express your answer using interval notation. Graph the solution.
14.
20 – 4(2 – x) ≤ −2𝑥
16. |1 − 2𝑥| − 4 < −1
1 3x  1 1
15.  

3
9
3
17.
−3|𝑥 + 4| + 15 ≥ −3
18. 2 8  2 x  4  28
BONUS: A circle of equation 2x 2  2y 2  12x  8y  6  0 is inscribed in a square. Find the area of the square.
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