Apply the Pythagorean Theorem to find the length between (2,7) and (−2, 0) Round your answer to the nearest hundredth, if necessary.(1 point)
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, the two given points (2, 7) and (-2, 0) can be thought of as the coordinates of two vertices of a right triangle. The length between these two points can be calculated as the hypotenuse of this right triangle.
To find the length between (2, 7) and (-2, 0), we need to calculate the length of the horizontal side (the base) and the length of the vertical side (the height) of the right triangle formed by these two points.
The length of the base can be calculated as the difference between the x-coordinates of the two points: -2 - 2 = -4.
The length of the height can be calculated as the difference between the y-coordinates of the two points: 0 - 7 = -7.
Next, we can use the Pythagorean Theorem to find the length between these two points:
Length^2 = base^2 + height^2
Length^2 = (-4)^2 + (-7)^2
Length^2 = 16 + 49
Length^2 = 65
Taking the square root of both sides, we find:
Length ≈ √65 ≈ 8.06
Therefore, the length between (2, 7) and (-2, 0) is approximately 8.06 units.
To find the length between two points using the Pythagorean Theorem, follow these steps:
1. Identify the coordinates of the two points. In this case, the first point is (2,7) and the second point is (-2, 0).
2. Use the coordinates to determine the difference in the x-coordinates (Δx) and the difference in the y-coordinates (Δy). For this example, Δx = (-2) - (2) = -4 and Δy = 0 - 7 = -7.
3. Apply the Pythagorean Theorem, which states that the square of the hypotenuse (the line connecting the two points) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the distance between the two points.
a^2 + b^2 = c^2
Substituting the values of Δx and Δy, we have:
(-4)^2 + (-7)^2 = c^2
Simplifying:
16 + 49 = c^2
65 = c^2
4. Take the square root of both sides to solve for c:
√65 = c
Rounding it to the nearest hundredth, c ≈ 8.06.
Therefore, the length between the points (2,7) and (-2, 0) is approximately 8.06 units.
To apply the Pythagorean Theorem to find the length between two points, we need to find the difference in x-coordinates and the difference in y-coordinates.
Given points:
Point 1: (2, 7)
Point 2: (-2, 0)
Difference in x-coordinates:
x2 - x1 = -2 - 2 = -4
Difference in y-coordinates:
y2 - y1 = 0 - 7 = -7
Now, we can apply the Pythagorean Theorem, which states that the square of the length of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the other two sides (a and b).
Using the formula:
c^2 = a^2 + b^2
Substituting the differences in coordinates:
c^2 = (-4)^2 + (-7)^2
c^2 = 16 + 49
c^2 = 65
To find the length (c), we need to take the square root of both sides:
c = √65
Rounded to the nearest hundredth, the length between the two points is approximately 8.06.