Apply the Pythagorean Theorem to find the length Between the two points (-2-1) and (2,4). round your answer to the nearest hundredth if necessary
To find the length 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.
So, considering the two given points as the vertices of a right triangle, the length between them is the hypotenuse. The other two sides of the right triangle can be calculated by subtracting the x-coordinates and y-coordinates, respectively.
Using this information, we can calculate the length between the two points as follows:
Length^2 = (x2 - x1)^2 + (y2 - y1)^2
Length^2 = (2 - (-2))^2 + (4 - (-1))^2
Length^2 = (4)^2 + (5)^2
Length^2 = 16 + 25
Length^2 = 41
Now, take the square root of both sides to find the length:
Length = √41
Length ≈ 6.40 (rounded to the nearest hundredth)
Therefore, the length between the two points (-2, -1) and (2, 4) is approximately 6.40 units.
To apply the Pythagorean Theorem to find the length between two points, you need to use the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2),
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the coordinates are (-2, -1) and (2, 4).
So, using the formula, you have:
d = √((2 - (-2))^2 + (4 - (-1))^2).
Simplifying this equation, you get:
d = √(4^2 + 5^2).
Further simplifying:
d = √(16 + 25).
d = √41.
To round the answer to the nearest hundredth, you can use a calculator or perform manual approximation:
√41 ≈ 6.40 (rounded to the nearest hundredth).
Therefore, the length between the two points is approximately 6.40 units.
To apply the Pythagorean Theorem and find the length between the two points (-2, -1) and (2, 4), we need to calculate the distance between their x-coordinates and y-coordinates.
First, find the difference in x-coordinates:
Δx = 2 - (-2) = 4
Next, find the difference in y-coordinates:
Δy = 4 - (-1) = 5
Now, we can use the Pythagorean Theorem formula, which is:
c^2 = a^2 + b^2
Here, c represents the length we want to find, and a and b are the differences in x and y coordinates, respectively.
Substituting the values:
c^2 = (4)^2 + (5)^2
c^2 = 16 + 25
c^2 = 41
To find c, take the square root of both sides:
c = √41
Rounding to the nearest hundredth, the length between the two points is approximately 6.40 units.