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
9.22
9.22
14
14
10
The length between (-1, 6) and (5, -2) can be found by using the Pythagorean Theorem. The formula is:
c^2 = (x2 - x1)^2 + (y2 - y1)^2
Plugging in the coordinates:
c^2 = (5 - (-1))^2 + (-2 - 6)^2
c^2 = (6)^2 + (-8)^2
c^2 = 36 + 64
c^2 = 100
Taking the square root of 100 gives us c = 10.
Therefore, the length between (-1, 6) and (5, -2) is 10 units.
To apply the Pythagorean theorem to find the length between (−1, 6) and (5, −2), follow these steps:
Step 1: Determine the horizontal distance between the two points.
The horizontal distance is the difference between the x-coordinates of the two points:
5 - (-1) = 6
Step 2: Determine the vertical distance between the two points.
The vertical distance is the difference between the y-coordinates of the two points:
-2 - 6 = -8
Step 3: Use the horizontal and vertical distances to calculate the length using the Pythagorean theorem.
The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the two other sides.
So, we have:
Length^2 = (horizontal distance)^2 + (vertical distance)^2
Length^2 = 6^2 + (-8)^2
Length^2 = 36 + 64
Length^2 = 100
Step 4: Take the square root of both sides to find the length:
Length = √100
Length = 10
Therefore, the length between (−1, 6) and (5, −2) is 10 units.
To apply the Pythagorean Theorem to find the length between two points, we need to find the horizontal distance (the difference between the x-coordinates) and the vertical distance (the difference between the y-coordinates) of the two points.
In this case, we have the points (-1, 6) and (5, -2).
The horizontal distance is calculated by subtracting the x-coordinate of one point from the x-coordinate of the other point:
Horizontal distance = 5 - (-1) = 6
The vertical distance is calculated by subtracting the y-coordinate of one point from the y-coordinate of the other point:
Vertical distance = -2 - 6 = -8
Notice that the vertical distance is negative because we disregarded the sign in the equation; we only need the magnitude.
Now that we have the horizontal and vertical distances, 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.
Applying the theorem, we have:
Length = √(horizontal distance² + vertical distance²)
Length = √(6² + (-8)²)
Length = √(36 + 64)
Length = √100
Length = 10
Therefore, the length between the points (-1, 6) and (5, -2) is 10 units.