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)
• 4.58
0 5.38
0 2.65
• 29
To find the length between two points using the Pythagorean theorem, we can use the formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the first point are (2, 5) and the coordinates of the second point are (7, 3).
Using the formula, we can calculate the distance as follows:
distance = √((7 - 2)^2 + (3 - 5)^2)
= √(5^2 + (-2)^2)
= √(25 + 4)
= √29
Rounding this to the nearest hundredth, we get 5.38.
Therefore, the length between the two points is approximately 5.38.
To apply the Pythagorean Theorem to find the distance between two points, you need to follow a few steps:
Step 1: Identify the coordinates of the two points. In this case, the coordinates are (2, 5) and (7, 3).
Step 2: Determine the difference between the x-coordinates and the y-coordinates. In this case, the difference in the x-coordinates is 7 - 2 = 5, and the difference in the y-coordinates is 3 - 5 = -2.
Step 3: Square each of the differences. In this case, squaring 5 gives 25, and squaring -2 gives 4.
Step 4: Add the squared differences together. In this case, 25 + 4 = 29.
Step 5: Take the square root of the sum. In this case, the square root of 29 is approximately 5.39.
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39. Rounding to the nearest hundredth, the answer is 5.38.
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)
• 10
• 9.22
• 100
20 14
To apply the Pythagorean Theorem to find the distance between two points, we need to calculate the length of the hypotenuse of a right triangle formed by the two points.
The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the two points are (2, 5) and (7, 3). We can consider the horizontal distance between the two points as the base of the right triangle and the vertical distance as the height.
The horizontal distance is 7 - 2 = 5 units.
The vertical distance is 3 - 5 = -2 units.
To calculate the length between the two points, we need to take the absolute value of the vertical distance since distance can't be negative.
Using the Pythagorean Theorem, we have:
Length^2 = (base)^2 + (height)^2
Length^2 = 5^2 + (-2)^2
Length^2 = 25 + 4
Length^2 = 29
To find the length, we take the square root of both sides:
Length = √29
Rounding the answer to the nearest hundredth, the final result is approximately 5.39.
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39 units.
To find the distance between two points using the Pythagorean theorem, we can use the formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the first point are (-1, 6) and the coordinates of the second point are (5, -2).
Using the formula, we can calculate the distance as follows:
distance = √((5 - (-1))^2 + (-2 - 6)^2)
= √((5 + 1)^2 + (-2 - 6)^2)
= √(6^2 + (-8)^2)
= √(36 + 64)
= √100
The square root of 100 is 10.
Therefore, the length between the two points is 10.