1.1Study Rotations

1. Plotting and transforming points, Scatter plots

4.

1. Plot the points on the coordinate plane to the righta. (-2, 4)

b. (5, 8)

c. ( 4½ , -3)

d. (-1, -5.5)

2. Label the points on the coordinate plane

a. A ( __________, ___________)

b. B ( __________, ___________)

c. C ( __________, ___________)

d. D ( __________, ___________)

e. E ( __________, ___________)

f. F ( __________, ___________)

3. Translate the points without graphinga. Translate the point A(2, 3) to point B by shifting 3 units right and 4 units up.

B= (___________, ______________)b. Translate the point B(-1, 2) to point C by shifting 2 units left and 2 units down.

C= (___________, ______________)

c. Translate the point C(0, 5) to point D by shifting 1 unit left and 8 units down.

D= (___________, ______________)

a. b. c.

d. e. f.

5.

6.

7.

1.1 Study Rotations2. Quadrants

Determine which quadrant(s) contain points under the following conditions.

8. x >3 , y >2 _______________________________________________________

9. x< 0 y < 5 _______________________________________________________

10. x = 1, y < 0 _______________________________________________________

11. x > 2, y = -3 _______________________________________________________

12. x > 0, -y < 0 _______________________________________________________

13. –x >0 , y < 0 _______________________________________________________

14. xy > 0 ______________________________________________________

15. –xy < 0 ______________________________________________________

1.1Study Rotations

3. Pythagorean Theorem and Distance Formula

Hypotenuse = Longest side(side across from the largest angle, which must be 90° angle)

16. Two legs of a right triangle are 4 and 5, what is the length of the hypotenuse?

17. The length of a leg of a right triangle is 10 while the hypotenuse is 25, what is the length of the other leg?

18. How far do you need to place a 15’ ladder so that it exactly reaches top of a 12’ wall?

19. An isosceles triangle has congruent sides of 20 cm. The base is 10 cm. What is the area of the triangle?

20. Jill’s front door is 42” wide and 84”tall. She purchased a circular table that is 96” in diameter. Will the table fit through the front door?

21. Find the distance between (-2, 3) and (3, -5)

22. Verify that the triangle is a right triangle if the vertices are: (4,5), (6,1), (10,3)

23. Verify that the vertices are that of an isosceles triangle: (-2, 4) , (3,-1), (-1,-3)

24. Find the coordinates of the points that are 10 units from the origin and have an x, coordinate of 6.

25. You are at Pritzker, which is the origin. Michocana is at point (-3, 2), McDonald’s is at (-2,-4). Which is closer to shcool?

1.1Study Rotations

4. Midpoints and Endpoints

26. What is the midpoint of (-3, 5) and (2, -2). Plot the endpoints and midpoint on the coordinate plane below.

27. If endpoint A is (2, 4) and the midpoint of AB is (3, 1), what is the ordered pair for endpoint B?

28. If endpoint A is (5, 2) and the midpoint of AB is (-10, -2), what is the ordered pair for endpoint B?

29. If endpoint A is (-1, 3) and the midpoint of AB is (2, -2), what is the ordered pair for endpoint B?

30. Find the point that is one fourth of the way from (2,4) to (10, 8)

31. In 2000, a store made a profit of $5,000 in January and in 2002 it made a profit of $12,350. Assuming its growth is linear from 2000 to 2002, what would you estimate the profit was in January of 2001?

1.1Study Rotations5. Volume

32. A cylinder with radius of 3 units has a volume of 86 cubic units. What is the height of the cylinder?

33. A tea infuser in the shape of a right rectangular pyramid is 8 cm tall and has a base of 3 cm long and 2 cm wide. To make the best tea, the infuser should be 80 percent filled with tea. What is the volume needed in cubic centimeters to fill to 80 percent capacity?

34. A kids toy is made up of a half-sphere perfectly beneath a cone sharing the circular base. If the radius is 10 cm and the height from the bottom of the sphere to the top of the cone 25 cm, what is the volume of the kids toy?

36. A rectangular shipping container has a volume of 2720 cubic feet. It’s face is 8ft x 8.5ft, what is the depth of the container.

37. A room is 3 times as wide as it is long and its area is 2739 square feet. a. Determine an equation to find the length of the room.

b. Approximately what is the length of the room rounded to the hundredths place.

c. Determine the perimeter of the room

d. If the height of the ceiling is half of its length, what is the air capacity (the volume) of the room?

37. A rectangular piece of paper is 11 cm long and 15 cm wide. A cylinder is formed by rolling the paper along its length. What is the volume of the cylinder?

1.1Study Rotations6. Ratios, Rates, and Proportions

38. A plumber has a type of liquid in 2-hectoagram containers. Based on the information below, how many 10mg vials can he make from the 2-hectogram container?

39. Karla’s family is selling mango at the upcoming street fair. Karla can peel at least 15 mangoes per hour and at most 22 mangoes per hour. At this rate, what is the maximum possible amount of hours it could take Karla to peel 80 mangoes?

40. How many pens can Alice buy with m dollars, if k pens cost n cents?a) n/100kmb) km/nc) nk/100md) 100km/ne) 100kmn

41. A manager at a store selects 5 products at random for inspection out of every 350 products. At this rate how many products will be inspected if the factory produces 30,000 products?

42. The amount of money a waiter earns is directly proportional to the number of tables he tends to. If he earns $140 a night where he tends to 9 tables, how much money will he earn on a night where he waits on 25 tables?

43. The distance traveled by Earth in one orbit around the sun is about 580,000,000miles. Earth makes one complete orbit around the sun in one year. What is the average speed of Earth, in miles per hour, as it orbits the Sun? Round to the nearest thousand.

1 hectogram = 100 grams1,000 milligrams = 1 gram