Apply the Pythagorean Theorem to find the length Between (-1,6) and (5,-2). Round your answer to the nearest hundredth if necessary.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
To find the distance between points (-1,6) and (5,-2), we need to treat these points as the coordinates of the endpoints of a right triangle in a coordinate plane.
Let's label the points: (-1,6) as point A and (5,-2) as point B.
The length of the horizontal side of the triangle (also known as the base or the difference in x-coordinates) is given by the absolute difference of the x-coordinates of the two points:
Δx = |5 - (-1)| = 6
The length of the vertical side of the triangle (also known as the height or the difference in y-coordinates) is given by the absolute difference of the y-coordinates of the two points:
Δy = |-2 - 6| = 8
Now, using the Pythagorean Theorem, we can find the length of the hypotenuse (the distance between points A and B):
c² = a² + b²
Plug in the values:
c² = 6² + 8²
c² = 36 + 64
c² = 100
Taking the square root of both sides:
c = √100
c = 10
Therefore, the length between points (-1,6) and (5,-2) is 10 units.
To apply the Pythagorean Theorem to find the length between two points, we need to follow these steps:
Step 1: Identify the coordinates of each point. In this case, the coordinates are:
Point 1: (-1, 6)
Point 2: (5, -2)
Step 2: Use the distance formula to calculate the length between the two points. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates, we substitute the values into the formula:
d = √((5 - (-1))^2 + (-2 - 6)^2)
d = √((5 + 1)^2 + (-2 - 6)^2)
d = √(6^2 + (-8)^2)
d = √(36 + 64)
d = √100
d = 10
Therefore, the length between the two points (-1, 6) and (5, -2) is 10 units.
To apply the Pythagorean Theorem to find the length between the points (-1, 6) and (5, -2), you need to follow these steps:
Step 1: Identify the coordinates of the two points.
The given points are (-1, 6) and (5, -2).
Step 2: Determine the difference in the x-coordinates and y-coordinates.
The difference in the x-coordinates is 5 - (-1) = 6.
The difference in the y-coordinates is -2 - 6 = -8.
Step 3: Square the differences.
Square the difference in the x-coordinates: (6)^2 = 36.
Square the difference in the y-coordinates: (-8)^2 = 64.
Step 4: Add the squared differences together.
The sum of the squared differences is 36 + 64 = 100.
Step 5: Take the square root of the sum to find the length.
The square root of 100 is 10.
Therefore, the length between the points (-1, 6) and (5, -2) is 10.