Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2) . Round your answer to the nearest hundredth, if necessary.
A. 9.22
B. 10
C. 14
D. 100
To find the length between two points using the Pythagorean Theorem, we can use the formula:
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Using the given points, we have:
x1 = -1 y1 = 6
x2 = 5 y2 = -2
Substituting these values into the formula, we get:
d = sqrt( (5 - (-1))^2 + (-2 - 6)^2 )
= sqrt( (6)^2 + (-8)^2 )
= sqrt( 36 + 64 )
= sqrt( 100 )
= 10
Therefore, the length between the two points is 10, which corresponds to option B.
To apply the Pythagorean Theorem to find the length between two points, we need to follow these steps:
1. Identify the coordinates of the two points: (-1, 6) and (5, -2).
2. Find the difference between the x-coordinates and the y-coordinates.
- Difference in x-coordinates: 5 - (-1) = 6
- Difference in y-coordinates: -2 - 6 = -8
3. Square each difference to eliminate negative signs and find the squares of these values.
- Squaring the difference in x-coordinates: 6^2 = 36
- Squaring the difference in y-coordinates: (-8)^2 = 64
4. Add the squares obtained in step 3.
- 36 + 64 = 100
5. Take the square root of the result obtained in step 4 to find the length between the two points.
- Square root of 100 = 10
So, the length between the points (-1, 6) and (5, -2) is 10.
Therefore, the correct option is B. 10.
To apply the Pythagorean Theorem, we need to calculate the distance between two points in a coordinate plane.
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.
Let's label the points as A and B:
A = (-1, 6)
B = (5, -2)
We can calculate the difference in x-coordinates and y-coordinates:
Δx = x2 - x1 = 5 - (-1) = 6
Δy = y2 - y1 = -2 - 6 = -8
Now, we can use the Pythagorean Theorem to find the length between A and B:
length^2 = Δx^2 + Δy^2
length^2 = 6^2 + (-8)^2
length^2 = 36 + 64
length^2 = 100
To find the length, we take the square root of both sides:
length = √100
length = 10
Therefore, the length between (-1, 6) and (5, -2) is approximately 10.
The answer is B. 10.