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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) ______________________________________________________________________________________________ ______________________________________________________________________________________________ ______________________________________________________________________________________________ 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 23 5 52 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.