Apply the Pythagorean Theorem to find the length Between the two points (2,-3) and (5,5). Round your answer to the nearest hundredth if necessary.
To find the length between two points (x1, y1) and (x2, y2), you can use the Pythagorean theorem formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's use this formula to find the length between the points (2, -3) and (5, 5):
x1 = 2
y1 = -3
x2 = 5
y2 = 5
d = √((5 - 2)^2 + (5 - (-3))^2)
= √(3^2 + 8^2)
= √(9 + 64)
= √73
Rounding to the nearest hundredth, the length between the two points is approximately 8.54.
To apply the Pythagorean Theorem to find the length between two points (x₁, y₁) and (x₂, y₂), you need to follow these steps:
1. Identify the coordinates of the two points:
Point 1: (x₁, y₁) = (2, -3)
Point 2: (x₂, y₂) = (5, 5)
2. Determine the horizontal and vertical distances between the points:
Horizontal distance = x₂ - x₁
Vertical distance = y₂ - y₁
In this case:
Horizontal distance = 5 - 2 = 3
Vertical distance = 5 - (-3) = 8
3. Apply the Pythagorean Theorem:
The Pythagorean theorem 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.
In this case, the horizontal and vertical distances serve as the two sides of the right triangle, and the length we are trying to find is the hypotenuse.
The formula is:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Plugging in the values:
c² = 3² + 8²
c² = 9 + 64
c² = 73
4. Find the square root to get the length of the hypotenuse (c):
c = √73
c ≈ 8.54 (rounded to the nearest hundredth)
Therefore, the length between the two points (2,-3) and (5,5) is approximately 8.54 units.
To find the length between the two points (2, -3) and (5, 5) using the Pythagorean Theorem, follow these steps:
Step 1: Find the difference in the x-coordinates.
x2 - x1 = 5 - 2 = 3
Step 2: Find the difference in the y-coordinates.
y2 - y1 = 5 - (-3) = 5 + 3 = 8
Step 3: Square the differences.
(3)^2 = 9
(8)^2 = 64
Step 4: Add the squared differences.
9 + 64 = 73
Step 5: Take the square root of the sum. Round your answer to the nearest hundredth if necessary.
√73 ≈ 8.54
Therefore, the length between the two points (2, -3) and (5, 5) is approximately 8.54 units.