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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 32 (y 7)2 49 11. Find the range of the circle 11. x 32 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 32 (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 ____________