Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) Round your answer to the nearest hundredth, if necessary.
To find the length between the points (2, 5) and (7, 3), we can use the Pythagorean Theorem.
First, we need to find the lengths of the horizontal and vertical sides of the right triangle formed by connecting the two points. The horizontal side is the difference in x-coordinates: 7 - 2 = 5. The vertical side is the difference in y-coordinates: 3 - 5 = -2.
Using the Pythagorean Theorem, we can calculate the length of the hypotenuse, which is the distance between the two points:
Length = √(horizontal side^2 + vertical side^2)
= √(5^2 + (-2)^2)
= √(25 + 4)
= √29
Rounding to the nearest hundredth, the length between the points (2, 5) and (7, 3) is approximately 5.39.
To find the length between the points (2, 5) and (7, 3) using the Pythagorean Theorem, follow these steps:
Step 1: Determine the difference in x-coordinates and y-coordinates:
Δx = x2 - x1 = 7 - 2 = 5
Δy = y2 - y1 = 3 - 5 = -2
Step 2: Square the differences:
Δx^2 = (5)^2 = 25
Δy^2 = (-2)^2 = 4
Step 3: Add the squared differences:
Δx^2 + Δy^2 = 25 + 4 = 29
Step 4: Take the square root of the sum to find the distance:
distance = √(Δx^2 + Δy^2) = √29
Rounding to the nearest hundredth, the length between the points is approximately 5.39.
To apply the Pythagorean Theorem to find the length between two points, we need to find the difference in x-coordinates (we'll call it Δx) and the difference in y-coordinates (we'll call it Δy). In this case, the coordinates are (2, 5) and (7, 3).
Δx = x₂ - x₁ = 7 - 2 = 5
Δy = y₂ - y₁ = 3 - 5 = -2
Next, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Using Δx and Δy as the lengths of the two sides, we have:
Length² = Δx² + Δy²
Plugging in the values we found:
Length² = 5² + (-2)²
Length² = 25 + 4
Length² = 29
Finally, we can find the length by taking the square root of both sides:
Length = √29
Rounded to the nearest hundredth, the length between (2, 5) and (7, 3) is approximately 5.39.
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)
To find the length between the points (-1, 6) and (5, -2), we can use the Pythagorean Theorem.
First, we need to find the lengths of the horizontal and vertical sides of the right triangle formed by connecting the two points. The horizontal side is the difference in x-coordinates: 5 - (-1) = 6. The vertical side is the difference in y-coordinates: -2 - 6 = -8.
Using the Pythagorean Theorem, we can calculate the length of the hypotenuse, which is the distance between the two points:
Length = √(horizontal side^2 + vertical side^2)
= √(6^2 + (-8)^2)
= √(36 + 64)
= √100
= 10
Rounding to the nearest hundredth, the length between the points (-1, 6) and (5, -2) is 10.00.