Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary.(1 point)
Responses
5.38
5.38
29
29
2.65
2.65
4.58
To find the distance between the points (2, 5) and (7, 3) using the Pythagorean Theorem, follow these steps:
Step 1: Find the difference in the x-coordinates (Δx):
Δx = x2 - x1
Δx = 7 - 2
Δx = 5
Step 2: Find the difference in the y-coordinates (Δy):
Δy = y2 - y1
Δy = 3 - 5
Δy = -2
Step 3: Calculate the square of Δx and Δy:
(Δx)^2 = 5^2 = 25
(Δy)^2 = (-2)^2 = 4
Step 4: Add the squares of Δx and Δy:
(Δx)^2 + (Δy)^2 = 25 + 4 = 29
Step 5: Take the square root of the sum:
Distance = √(29) ≈ 5.38
Therefore, the distance between the points (2, 5) and (7, 3) is approximately 5.38.
To find the length between two points using the Pythagorean Theorem, we need to calculate the distance between their x-coordinates and y-coordinates.
The formula for the distance between two points (x1, y1) and (x2, y2) is as follows:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's apply this formula to find the length between (2, 5) and (7, 3).
First, let's find the difference between the x-coordinates:
x2 - x1 = 7 - 2 = 5
Next, let's find the difference between the y-coordinates:
y2 - y1 = 3 - 5 = -2
Now, let's plug these values into the formula:
distance = sqrt((5)^2 + (-2)^2) = sqrt(25 + 4) = sqrt(29)
To round the answer to the nearest hundredth, we get:
distance ≈ 5.38
Therefore, the length between (2, 5) and (7, 3) is approximately 5.38.
To find the distance between the points (-1, 6) and (5, -2) using the Pythagorean Theorem, follow these steps:
Step 1: Find the difference in the x-coordinates (Δx):
Δx = x2 - x1
Δx = 5 - (-1)
Δx = 6
Step 2: Find the difference in the y-coordinates (Δy):
Δy = y2 - y1
Δy = -2 - 6
Δy = -8
Step 3: Calculate the square of Δx and Δy:
(Δx)^2 = 6^2 = 36
(Δy)^2 = (-8)^2 = 64
Step 4: Add the squares of Δx and Δy:
(Δx)^2 + (Δy)^2 = 36 + 64 = 100
Step 5: Take the square root of the sum:
Distance = √(100) = 10
Therefore, the distance between the points (-1, 6) and (5, -2) is 10.
To find the length between the points (-2, -1) and (2, 4) using the Pythagorean Theorem, follow these steps:
Step 1: Find the difference in the x-coordinates (Δx):
Δx = x2 - x1
Δx = 2 - (-2)
Δx = 4
Step 2: Find the difference in the y-coordinates (Δy):
Δy = y2 - y1
Δy = 4 - (-1)
Δy = 5
Step 3: Calculate the square of Δx and Δy:
(Δx)^2 = 4^2 = 16
(Δy)^2 = 5^2 = 25
Step 4: Add the squares of Δx and Δy:
(Δx)^2 + (Δy)^2 = 16 + 25 = 41
Step 5: Take the square root of the sum:
Distance = √(41) ≈ 6.40
Therefore, the length between the points (-2, -1) and (2, 4) is approximately 6.40.
To find the length between the points (2, -3) and (5, 5) using the Pythagorean Theorem, follow these steps:
Step 1: Find the difference in the x-coordinates (Δx):
Δx = x2 - x1
Δx = 5 - 2
Δx = 3
Step 2: Find the difference in the y-coordinates (Δy):
Δy = y2 - y1
Δy = 5 - (-3)
Δy = 8
Step 3: Calculate the square of Δx and Δy:
(Δx)^2 = 3^2 = 9
(Δy)^2 = 8^2 = 64
Step 4: Add the squares of Δx and Δy:
(Δx)^2 + (Δy)^2 = 9 + 64 = 73
Step 5: Take the square root of the sum:
Distance = √(73) ≈ 8.54
Therefore, the length between the points (2, -3) and (5, 5) is approximately 8.54.
Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2) . Round your answer to the nearest hundredth, if necessary.(1 point)
Responses
100
100
14
14
9.22
9.22
10
Use the image to answer the question.
A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Unlabeled data points marked are at left parenthesis negative 2 comma negative 1 right parenthesis, and at left parenthesis 2 comma 4 right parenthesis. A straight line joins the two lines with a positive slope.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
6:40
6:40
9
9
5.57
5.57
41
41
Use the image to answer the question.
A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Data points marked are point A at left parenthesis 2 comma negative 3 right parenthesis, and point B at left parenthesis 5 comma 5 right parenthesis.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
8.54
8.54
73
73
11
11
7.62