apply the pythagorean theorem to find the length between the two points (2,4) (-2, -1). round your answer to the nearest hundredth if necessary
The distance between two points (x1, y1) and (x2, y2) can be found using the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two points are (2, 4) and (-2, -1). The x-coordinates of the two points differ by 2 - (-2) = 4, and the y-coordinates differ by 4 - (-1) = 5.
The length between the two points can be found using the Pythagorean theorem as follows:
Distance = sqrt((4 - (-2))^2 + (5)^2)
Distance = sqrt(6^2 + 5^2)
Distance = sqrt(36 + 25)
Distance = sqrt(61)
Rounded to the nearest hundredth, the distance between the two points is approximately 7.81.
To apply the Pythagorean Theorem to find the length between two points (2,4) and (-2, -1), you need to calculate the distance between the two points using the formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Where:
(x₁, y₁) is the coordinates of the first point (2,4)
(x₂, y₂) is the coordinates of the second point (-2, -1)
d is the distance between the two points.
Let's substitute the values into the formula:
d = √((-2 - 2)² + (-1 - 4)²)
First, calculate inside the parentheses for each term to get:
d = √((-4)² + (-5)²)
Next, square each term:
d = √(16 + 25)
Add the numbers inside the square root:
d = √41
Finally, approximate the square root of 41 to the nearest hundredth:
d ≈ 6.40
Therefore, the length between the two points (2,4) and (-2, -1) is approximately 6.40 (rounded to the nearest hundredth).
To apply the Pythagorean Theorem to find the length between the two points (2,4) and (-2,-1), follow these steps:
Step 1: Find the horizontal distance (x-coordinate difference) between the two points.
To find the horizontal distance, subtract the x-coordinate of one point from the x-coordinate of the other point:
Horizontal distance = x2 - x1 = -2 - 2 = -4
Step 2: Find the vertical distance (y-coordinate difference) between the two points.
To find the vertical distance, subtract the y-coordinate of one point from the y-coordinate of the other point:
Vertical distance = y2 - y1 = -1 - 4 = -5
Step 3: Use the Pythagorean Theorem to find the length between the two points.
The Pythagorean Theorem states that the sum of the squares of the legs (horizontal and vertical distances) is equal to the square of the hypotenuse (length). In this case, the legs are the horizontal and vertical distances, and the hypotenuse is the length between the two points.
Length = sqrt((Horizontal distance)^2 + (Vertical distance)^2)
= sqrt((-4)^2 + (-5)^2)
= sqrt(16 + 25)
= sqrt(41)
Therefore, the length between the two points (2,4) and (-2,-1) is approximately sqrt(41). Rounded to the nearest hundredth, the length is approximately 6.40.