Question
The image below shows two cities, city A and city B. Which city is furthest away from the city center located at (0,0), and how far away is that city from the city center? Each square represents 1 mile. Point A is at (4, 5) and point B is at (-4, -5)
Responses
City A is furthest away. It is approximately 6.4 miles away
City A is furthest away. It is approximately 6.4 miles away
They are the same distance away.
They are the same distance away.
City B is furthest away. It is 8 miles away.
City B is furthest away. It is 8 miles away.
City B is furthest away. It is approximately 5.8 miles away.
City B is furthest away. It is approximately 5.8 miles away.
City A is furthest away. It is 3 miles away
ChatGPT
City B is furthest away from the city center located at (0,0), and it is approximately 8 miles away.
The correct answer is: City B is furthest away from the city center located at (0,0), and it is approximately 8 miles away.
55√in
5 square root of 5 in
155√in
15 square root of 5 in
105√in
10 square root of 5 in
265√in
26 square root of 5 in
The value of 55√in is approximately 9.35 inches (rounded to two decimal places).
The value of 5√5 in is approximately 5.59 inches (rounded to two decimal places).
The value of 155√in is approximately 24.75 inches (rounded to two decimal places).
The value of 15√5 in is approximately 10.61 inches (rounded to two decimal places).
The value of 105√in is approximately 16.64 inches (rounded to two decimal places).
The value of 10√5 in is approximately 7.07 inches (rounded to two decimal places).
The value of 265√in is approximately 41.94 inches (rounded to two decimal places).
The value of 26√5 in is approximately 18.24 inches (rounded to two decimal places).
User
A rectangle is shown in the figure below. What is the perimeter? Units are in inches.
Point A: (1, -1) Point B: (-3, 1) Point C: (3, 4) Point D: (7, 2) 55√in
5 square root of 5 in
155√in
15 square root of 5 in
105√in
10 square root of 5 in
265√in
26 square root of 5 in
To find the perimeter of the rectangle, we need to calculate the distance between consecutive points and then add them up.
Using the distance formula, the distances between the points are as follows:
- Distance AB = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(-3 - 1)^2 + (1 - (-1))^2]
= √[(-4)^2 + (2)^2]
= √[16 + 4]
= √20
= 2√5
- Distance BC = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(3 - (-3))^2 + (4 - 1)^2]
= √[(6)^2 + (3)^2]
= √[36 + 9]
= √45
= 3√5
- Distance CD = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(7 - 3)^2 + (2 - 4)^2]
= √[(4)^2 + (-2)^2]
= √[16 + 4]
= √20
= 2√5
- Distance DA = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(7 - 1)^2 + (2 - (-1))^2]
= √[(6)^2 + (3)^2]
= √[36 + 9]
= √45
= 3√5
Now, calculating the perimeter:
Perimeter = AB + BC + CD + DA
= 2√5 + 3√5 + 2√5 + 3√5
= (2 + 3 + 2 + 3)√5
= 10√5
Therefore, the perimeter of the rectangle is 10√5 inches.
Point A: (1, -1) Point B: (-3, 1) Point C: (3, 4) Point D: (7, 2)
Step 1: Find the
________of the line that connects A to B and the line that connects _______
.
Once these are found, we will _________
these.
The final answer is __ ______
Answer Choices to pick from: midpoint, adjacaent, square root, distance, d to c, b to d, c to d, a to b, multiply, add, divide, subtract, multiply each by 2 then add, 25, 30, 50, 55, yards, square yards, cubic yards
Step 1: Find the distance of the line that connects A to B and the line that connects C to D.
- Distance AB: √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(-3 - 1)^2 + (1 - (-1))^2]
= √[(-4)^2 + (2)^2]
= √[16 + 4]
= √20
= 2√5
- Distance CD: √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(7 - 3)^2 + (2 - 4)^2]
= √[(4)^2 + (-2)^2]
= √[16 + 4]
= √20
= 2√5
Step 2: Add these distances.
Sum of distances: 2√5 + 2√5 = 4√5
The final answer is 4√5.
Note: The answer choices provided do not accurately match the process and answer for this question.
You live at point A and your friend lives at point D. You let your friend borrow your calculator but you need it for tomorrow! You need to meet in the middle of your two houses. Which point do you meet at? Point A: (1, -1) Point B: (-3, 1) Point C: (3, 4) Point D: (7, 2)
To find the midpoint between two points, we can use the midpoint formula:
Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
Let's calculate the midpoint between points A and D:
Midpoint = ( (1 + 7) / 2 , (-1 + 2) / 2 )
= ( 8 / 2 , 1 / 2 )
= ( 4 , 0.5 )
Therefore, the midpoint between points A and D is (4, 0.5). This is the point where you and your friend should meet.
To determine which city is furthest away from the city center located at (0, 0), we can calculate the distance between each city and the city center using the distance formula.
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
For city A, the coordinates are (4, 5). Substituting these values into the distance formula, we get:
d_A = √((4 - 0)^2 + (5 - 0)^2)
= √(16 + 25)
= √41
≈ 6.4 miles
For city B, the coordinates are (-4, -5). Substituting these values into the distance formula, we get:
d_B = √((-4 - 0)^2 + (-5 - 0)^2)
= √(16 + 25)
= √41
≈ 6.4 miles
Therefore, both City A and City B are approximately 6.4 miles away from the city center.