Accelerated Coordinate Alg / Analytic Geometry A Readiness Packet This packet is not required, but students are highly encouraged to complete it and check their answers. Students entering Acc Coord Alg / Analytic Geom should have mastery of this material in order to be successful in the HS credit class. The material in this packet is in addition to the material found in the “Coordinate Algebra Readiness Packet.” If you have any questions, feel free to email me at [email protected]. Amanda Wilhelm Math Department Chair TRANSOFRMATIONS, CONGRUENCE, AND SIMILARITY 1. 2. 3. 4. 5. 6. A figure is dilated by a scale factor of 3. If the origin is the center of dilation, what is the image of the vertex located at (3, 4)? A figure is transformed. What transformation occurred? A( 7, 3) B(5, -3) C(3, 0) A’ (-7, 3) B (-5, -3) C(-3, 0) Which transformation would not necessarily result in congruent figures? What are the coordinates of Point S after a translation of 4 units to the right and 5 units down the coordinate for S is (-4, 2)? In a movie, a two-year-old boy is enlarged to a height of 112 feet. If the average height of a twoyear-old is 3 feet, what is the scale factor? A nine ft street sign casts a shadow that is 12 ft long. The lamppost next to it casts a shadow that is 24 ft long. How tall is the lamppost? SQUARES AND SQUARE ROOTS Find the square root(s) of each number or simplify the expression. 7. 144 8. 256 9. 1 81 10. √25 + 10 11. 8 − √64 16 12. √ 4 + √4 13. A square picture frame measures 36 inches on each side. The actual wood trim is 2 inches wide. The photograph in the frame is surrounded by a bronze mat that measures 5 inches. What is the maximum side length for the photograph? What is the maximum area of the photograph? Approximate each square root to the nearest tenth. 14. √34 15. √82 16. √71 17. √24 SOLVING EQUATIONS FROM WORD PROBLEMS 18. Carpet Plus installs carpet for $100 plus $8 per square yard. Carpet World charges $75 for installation and $10 per square yard. Find the number of square yards when the cost is the same. 19. When 15 is added to twice a number, the result is the same as when 3 is added to 5 times a number. What is the number? 20. Six times a number increased by 12 plus 3 times the same number increased by 6 is equal to 58.5. What is the number? 21. The perimeter of a rectangle is 4.8 m. Its length is twice its width. How wide is the garden? 22. Five dollars more than half the price of a sweater is equal to $40.39. What is the full price of the sweater? 23. If you add 8 to a number divided by five, the sum is 8. What is the number? FUNCTIONS Determine if each relation is a function. 24. X Y 25. (1, 3), (2,5), (3, 0), (4, -1), (5, 5) 6 75 7 80 8 87 7 88 9 95 26. X Y 27. (2, 7), (6, 4), (0, 3), (2, 6), (1, 5) 1 4 2 8 3 12 4 16 5 20 28-30 Graph the following linear functions on a coordinate plane. 28. y = 3x + 4 29. -2x + 3y = -6 30. -3x – 4y = 12 31. Seth receives $100 from his grandmother for his birthday. He also saves $20 every month. Write an equation relating total savings in terms of the number of months. In 32-35, find the slope of the line that passes through each pair of coordinates. 32. (-2, -8), (1, 4) 33. (-3, 4), (3, -4) 34. (3, 2), (3, -2) 35. (4, 1), (-2, 1) 36. Write an equation in slope intercept form of a line that passes through (7, 4) and (4, 8).