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 formula derived from the Pythagorean theorem:
distance = square root of ((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1, y1) = (-1, 6) and (x2, y2) = (5, -2). Plugging these values into the formula, we get:
distance = square root of ((5 - (-1))^2 + (-2 - 6)^2)
= square root of ((5 + 1)^2 + (-2 - 6)^2)
= square root of (6^2 + (-8)^2)
= square root of (36 + 64)
= square root of 100
= 10
Therefore, the length between the points (-1, 6) and (5, -2) is 10.
To find the length between two points using the Pythagorean Theorem, we need to first identify the coordinates of the two points. In this case, the coordinates of the first point are (-1, 6) and the coordinates of the second point are (5, -2).
The Pythagorean Theorem 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 lengths of the other two sides.
In this case, we can use the distance formula, which is derived from the Pythagorean Theorem, to find the length between the two points. The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) represents the coordinates of the first point and (x2, y2) represents the coordinates of the second point.
Applying the distance formula to the given points, we have:
d = √((5 - (-1))^2 + (-2 - 6)^2)
Simplifying this expression further:
d = √((6)^2 + (-8)^2)
= √(36 + 64)
= √100
= 10
Therefore, the length between the points (-1, 6) and (5, -2) is 10 units.
To find the length between two points using the Pythagorean Theorem, you need to calculate the distance between their x-coordinates and y-coordinates, and then use the formula:
Distance = √(Δx² + Δy²)
Given the coordinates of the two points: (-1, 6) and (5, -2), we can find the distance between them by following these steps:
Step 1: Calculate Δx (the difference between the x-coordinates):
Δx = x2 - x1 = 5 - (-1) = 6
Step 2: Calculate Δy (the difference between the y-coordinates):
Δy = y2 - y1 = (-2) - 6 = -8
Step 3: Calculate Δx² and Δy²:
Δx² = 6² = 36
Δy² = (-8)² = 64
Step 4: Substitute the values into the formula and calculate the distance:
Distance = √(Δx² + Δy²) = √(36 + 64) = √100 = 10
The distance between the two points is 10 units.