1. Point B has coordinates (2,1). The x-coordinate of point A is −10. The distance between point A and point B is 15 units. What are the possible coordinates of point A? Write an ordered pair. Use a comma to separate answers as needed.
2. Point B has coordinates (−4,−2). The x-coordinate of point A is 5. The distance between point A and point B is 12 units.
a. What are the possible coordinates of point A?
b. Find the possible coordinates of point A if point B were moved to (−2,−4).
3. A square pyramid has base edge length 22 ft. The slant height of the pyramid is 61 ft. What is the volume of the pyramid?
4. What is the longest line segment that can be drawn in a right rectangular prism that is 16 cm long, 9 cm wide, and 7 cm tall? Round to one decimal place as needed.
5.
a. What is true about the longest distance between any two vertices in a right rectangular prism that is 14 cm long, 13 cm wide, and 8 cm high? Select all that apply.
A. The distance is the square root of the sum of the two longest lengths squared.
B. The distance is greater than 14 cm.
C. The distance can be found using the Pythagorean Theorem.
D. The distance is at most 14 cm.
b. Find the longest distance between any two vertices in this right rectangular prism. Round to one decimal place as needed.
6. Point A has coordinates (4,1). The x-coordinate of point B is 7. The distance between point A and point B is 5 units. Your friend says the coordinates of point B could be (8,4).
a. What are the possible coordinates of point B? Write an ordered pair. Use a comma to separate answers as needed.
b. What mistake did your friend make?
A. Your friend moved the correct distance but the incorrect direction on the coordinate plane.
B. Your friend used the given distance as one of the leg lengths instead of the hypotenuse length.
C. Your friend switched the hypotenuse length for one of the leg lengths.
D. Your friend's point does not have the same x-coordinate as point A. Your friend switched the leg lengths of the right triangle.
7. You are painting a square pyramid for a diorama. The square pyramid has base edge length 10 in. The height of the pyramid is 12 in.
a. Find the surface area of the square pyramid.
b. You have enough paint to cover 400 in.^{2}. Do you have enough paint for the pyramid?
8. Point A has coordinates (1,0). The x-coordinate of point B is 4. The distance between point A and point B is 5 units. What are the possible coordinates of point B? Write an ordered pair. Use a comma to separate answers as needed.