Apply the Pythagorean theorem define length between the two points (3,2) and (7,8). How do you answer to the nearest hundredth
To find the length between the two points using the Pythagorean theorem, we need to consider the distance between their x-coordinates and y-coordinates.
The x-coordinate difference is: 7 - 3 = 4
The y-coordinate difference is: 8 - 2 = 6
Now, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Thus, the length between the two points is given by the square root of the sum of the squares of the differences:
Length = √((4)^2 + (6)^2)
= √(16 + 36)
= √52
≈ 7.21 (rounded to the nearest hundredth)
Therefore, the length between the points (3,2) and (7,8) is approximately 7.21.
To find the length between two points using the Pythagorean theorem, we need to find the difference in the x-coordinates and the difference in the y-coordinates of the two points.
The coordinates of the first point are (3, 2), and the coordinates of the second point are (7, 8).
The difference in the x-coordinates is: (7 - 3) = 4
The difference in the y-coordinates is: (8 - 2) = 6
Now we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, a and b represent the differences in the x and y coordinates, and c represents the length between the points.
So, using the formula, we have:
c^2 = a^2 + b^2
c^2 = 4^2 + 6^2
c^2 = 16 + 36
c^2 = 52
To find c, we take the square root of both sides:
c = √52
c ≈ 7.21
Therefore, the length between the points (3, 2) and (7, 8) is approximately 7.21 units when rounded to the nearest hundredth.
To find the length between two points using the Pythagorean theorem, follow these steps:
1. Identify the coordinates of the two points. Let's call the first point (x1, y1) and the second point (x2, y2).
In this case, the first point is (3, 2) and the second point is (7, 8).
2. Calculate the difference in x-coordinates and y-coordinates.
Δx = x2 - x1
Δy = y2 - y1
In this case, Δx = 7 - 3 = 4 and Δy = 8 - 2 = 6.
3. Square the difference in x-coordinates and y-coordinates.
(Δx)^2 = 4^2 = 16
(Δy)^2 = 6^2 = 36
4. Use the Pythagorean theorem formula.
Distance = √((Δx)^2 + (Δy)^2)
Distance = √(16 + 36)
5. Simplify the equation and calculate the square root.
Distance = √52
6. Round the answer to the nearest hundredth.
Distance ≈ 7.21 (to the nearest hundredth)
Therefore, the length between the points (3, 2) and (7, 8) is approximately 7.21 units.