(-2, -1) and (2, 4)
apply the pythagorean thereom to find the length between the two points round the naswer to the nearest hundreth if neccary
To find the distance between the two points (-2, -1) and (2, 4), we can use the Pythagorean theorem.
The Pythagorean theorem states that in a 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, we can consider the distance between the two points as the hypotenuse of a right triangle. The other two sides would be the horizontal and vertical distances between the points.
The horizontal distance = 2 - (-2) = 4
The vertical distance = 4 - (-1) = 5
Now, apply the Pythagorean theorem:
Distance^2 = (horizontal distance)^2 + (vertical distance)^2
Distance^2 = 4^2 + 5^2
Distance^2 = 16 + 25
Distance^2 = 41
Taking the square root of both sides:
Distance = √41
Rounding to the nearest hundredth:
Distance ≈ 6.40 (rounded to the nearest hundredth)
(2,-3) and (5,5)
apply the pythagorean theorem to find the length between the two points round the answer to the nearest hundredth if necessary
To find the distance between the two points (2, -3) and (5, 5), we can use the Pythagorean theorem.
The Pythagorean theorem states that in a 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, we can consider the distance between the two points as the hypotenuse of a right triangle. The other two sides would be the horizontal and vertical distances between the points.
The horizontal distance = 5 - 2 = 3
The vertical distance = 5 - (-3) = 8
Now, apply the Pythagorean theorem:
Distance^2 = (horizontal distance)^2 + (vertical distance)^2
Distance^2 = 3^2 + 8^2
Distance^2 = 9 + 64
Distance^2 = 73
Taking the square root of both sides:
Distance = √73
Rounding to the nearest hundredth:
Distance ≈ 8.54 (rounded to the nearest hundredth)
the answers are
1. 2.83
2. 5.39
3. 10
4. 6:40
5. 8.54
Apologies for the confusion. Let's go through the calculations again.
Given points: (2, -3) and (5, 5)
The horizontal distance = 5 - 2 = 3
The vertical distance = 5 - (-3) = 8
Now, apply the Pythagorean theorem:
Distance^2 = (horizontal distance)^2 + (vertical distance)^2
Distance^2 = 3^2 + 8^2
Distance^2 = 9 + 64
Distance^2 = 73
Taking the square root of both sides:
Distance ≈ √73
Rounding to the nearest hundredth:
Distance ≈ 8.54 (rounded to the nearest hundredth)
So, the correct answer is 8.54.
To find the length between two points using the Pythagorean Theorem, you need to calculate the distance between their respective x-coordinates and y-coordinates, and then use these values to determine the hypotenuse of a right-angled triangle.
Let's start by calculating the horizontal distance between the two points:
Distance on the x-axis = |x2 - x1|
= |2 - (-2)|
= |2 + 2|
= 4
Next, we'll calculate the vertical distance between the two points:
Distance on the y-axis = |y2 - y1|
= |4 - (-1)|
= |4 + 1|
= 5
Now, using these distances, we can apply the Pythagorean Theorem.
Length between the two points = sqrt((Distance on the x-axis)^2 + (Distance on the y-axis)^2)
= sqrt(4^2 + 5^2)
= sqrt(16 + 25)
= sqrt(41)
≈ 6.40 (rounded to the nearest hundredth)
Therefore, the length between the points (-2, -1) and (2, 4) rounded to the nearest hundredth is approximately 6.40.