1.What is the perimeter of △PQR
with vertices P(-9,2), Q(-7,3) and R(3,2) . Round your answer to the nearest tenth.
a 24.2
b19.8
c 27.6
d 5.6
2. You are tiling a kitchen floor that is 13 ft. wide by 4 yd. long. How many square yards of tile do you need?(1 point)
a13 1/3yd^2
b17 1/3yd^2
c52yd^2
d40yd^2
3.The diameter of circle Z is 7 in. What is the area in terms of π
?(1 point)
a 7
b12.25
c 3.5
d 8
4. Find the midpoint of AB
if A(-3,8) and B(-7,- 6).(1 point)
a(-1,-5)
b(1,-5)
c (5,1)
d(-5,-1)
5.The midpoint of CD¯¯¯¯¯¯¯¯
is E (2, -1). One endpoint is C (-9,4). What are the coordinates of the other endpoint?(1 point)
a(13,-6)
b(7,-2)
c(-3.5,1.5)
d(8,-3)
6.Find the distance between the points (-8, -2) and (6, -1). Round to the nearest tenth(1 point)
unit =
1. To find the perimeter of △PQR, we need to find the length of each side and add them together.
The length PQ can be found using the distance formula:
√((-7 - (-9))^2 + (3 - 2)^2) = √(2^2 + 1^2) = √(4 + 1) = √5
The length QR can be found using the distance formula:
√((3 - (-7))^2 + (2 - 3)^2) = √(10^2 + 1^2) = √(100 + 1) = √101
The length RP can be found using the distance formula:
√((-9 - 3)^2 + (2 - 2)^2) = √((-6)^2 + 0^2) = √(36 + 0) = √36 = 6
Adding the three side lengths together: √5 + √101 + 6 ≈ 19.8
Therefore, the perimeter of △PQR is approximately 19.8. Therefore, the correct answer is (b) 19.8.
2. To find the area of the kitchen floor in square yards, we need to convert the width and length to the same unit.
13 ft = 13/3 yd (since 1 yard = 3 feet)
The length is already given in yards.
The area of the kitchen floor is then calculated by multiplying the width and length:
(13/3) yd × 4 yd = 52 yd^2
Therefore, you need 52 square yards of tile. The correct answer is (c) 52yd^2.
3. The area of a circle can be calculated using the formula A = πr^2, where r is the radius of the circle.
The radius of circle Z is half the diameter, so r = 7/2 inches.
The area of circle Z is then:
A = π(7/2)^2 = π(49/4) = 49π/4
Therefore, area of the circle in terms of π is 49π/4. The correct answer is (b) 12.25.
4. To find the midpoint of AB, we need to find the average of the x-coordinates and the average of the y-coordinates.
The x-coordinate of the midpoint is the average of the x-coordinates of A and B:
(-3 + (-7))/2 = -10/2 = -5
The y-coordinate of the midpoint is the average of the y-coordinates of A and B:
(8 + (-6))/2 = 2/2 = 1
Therefore, the midpoint of AB is (-5, 1). The correct answer is (d) (-5,-1).
5. The midpoint of CD is (2, -1). One endpoint is C (-9, 4).
The x-coordinate of the other endpoint is found by subtracting the x-coordinate of the midpoint from the x-coordinate of C:
x = -9 - 2 = -11
The y-coordinate of the other endpoint is found by subtracting the y-coordinate of the midpoint from the y-coordinate of C:
y = 4 - (-1) = 5
Therefore, the coordinates of the other endpoint are (-11, 5). The correct answer is (a) (13,-6).
6. To find the distance between two points, we use the distance formula:
√((6 - (-8))^2 + (-1 - (-2))^2) = √(14^2 + 1^2) = √(196 + 1) = √197
Rounded to the nearest tenth, the distance between the points is approximately 14.0. The correct answer is 14.0.
1. To find the perimeter of △PQR, we need to find the length of each side and then add them together.
The distance formula is used to find the distance between two points, which is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the distance formula, we can find the length of each side of the triangle:
Side PQ: d = √((-7 - (-9))^2 + (3 - 2)^2) = √(2^2 + 1^2) = √(4 + 1) = √5
Side QR: d = √((3 - (-7))^2 + (2 - 3)^2) = √(10^2 + (-1)^2) = √(100 + 1) = √101
Side PR: d = √((3 - (-9))^2 + (2 - 8)^2) = √(12^2 + (-6)^2) = √(144 + 36) = √180 = 6√5
Next, we add up the length of each side:
Perimeter of △PQR = PQ + QR + PR = √5 + √101 + 6√5
To the nearest tenth, the perimeter is approximately 27.6.
Therefore, the answer is (c) 27.6.
2. To find the number of square yards of tile needed to tile the kitchen floor, we need to convert the dimensions from feet to yards and then multiply the lengths:
Width of the floor = 13 ft
Length of the floor = 4 yd
To convert 13 ft to yards, we divide by 3 (since there are 3 feet in a yard):
13 ft ÷ 3 = 4.33 yd (rounded to the nearest hundredth)
Now, we can multiply the width and length to find the area:
Area of the floor = 4.33 yd * 4 yd = 17.32 yd^2
To the nearest third, the area is approximately 17 1/3 yd^2.
Therefore, the answer is (b) 17 1/3 yd^2.
3. The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle.
In this case, the diameter of circle Z is given as 7 in. The radius is half of the diameter, so the radius of circle Z is 7/2 = 3.5 in.
Using the formula for the area of a circle:
Area of circle Z = π * (3.5 in)^2 = π * 12.25 in^2
Therefore, the area is 12.25π.
Therefore, the answer is (b) 12.25π.
4. To find the midpoint of AB, we need to find the average of the x-coordinates and the average of the y-coordinates of points A(-3,8) and B(-7,-6).
The midpoint formula is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Using the given points:
Midpoint = ((-3 + -7)/2, (8 + -6)/2) = (-10/2, 2/2) = (-5, 1)
Therefore, the midpoint of AB is (-5, 1).
Therefore, the answer is (d) (-5, -1).
5. We are given the midpoint E(2, -1) and one endpoint C(-9, 4) of the line segment CD.
To find the other endpoint, we can use the midpoint formula and solve for the missing endpoint coordinates.
The midpoint formula is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Using the given midpoint E(2, -1) and endpoint C(-9, 4):
(2, -1) = ((-9 + x)/2, (4 + y)/2)
By comparing the x-coordinates and y-coordinates separately, we can solve for x and y:
-9 + x = 2 * 2 -> -9 + x = 4 -> x = 13
4 + y = 2 * (-1) -> 4 + y = -2 -> y = -6
Therefore, the coordinates of the other endpoint are (13, -6).
Therefore, the answer is (a) (13, -6).
6. To find the distance between the points (-8, -2) and (6, -1), we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given points:
d = √((6 - (-8))^2 + (-1 - (-2))^2) = √((6 + 8)^2 + (-1 + 2)^2) = √(14^2 + 1^2) = √(196 + 1) = √197
To the nearest tenth, the distance is approximately 14.
Therefore, the answer is 14.