apply the pythagorean theorem to find the length between the two points (2,4) (-5 , -2). round your answer to the nearest hundredth if necessary
To apply the Pythagorean theorem, we need to find the lengths of the two legs of a right triangle using the coordinates of the given points.
The formula for the distance between two points in a coordinate plane is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the points (2, 4) and (-5, -2), we can substitute the coordinates into the formula:
d = √((-5 - 2)^2 + (-2 - 4)^2)
Simplifying the equation:
d = √((-7)^2 + (-6)^2)
d = √(49 + 36)
d = √85
Rounding to the nearest hundredth:
d ≈ 9.22
Therefore, the length between the two points (2, 4) and (-5, -2) is approximately 9.22.
To apply the Pythagorean theorem to find the length between two points, you need to calculate the distance between their x-coordinates and their y-coordinates, and then apply the theorem using the formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For the two given points (2,4) and (-5,-2), the x-coordinate of the first point is 2 and the y-coordinate is 4. The x-coordinate of the second point is -5 and the y-coordinate is -2.
Using the formula, you can calculate the distance between these points as follows:
Distance = √((-5 - 2)^2 + (-2 - 4)^2)
= √((-7)^2 + (-6)^2)
= √(49 + 36)
= √85
Rounding the answer to the nearest hundredth, the length between the points (2,4) and (-5,-2) is approximately 9.22 units.
To apply the Pythagorean theorem to find the length between the two points (2,4) and (-5,-2), follow these steps:
Step 1: Determine the distance between the x-coordinates of the two points:
Δx = x₁ - x₂
= 2 - (-5)
= 7
Step 2: Determine the distance between the y-coordinates of the two points:
Δy = y₁ - y₂
= 4 - (-2)
= 6
Step 3: Use the Pythagorean theorem to find the length (d) between the two points:
d = √(Δx² + Δy²)
= √(7² + 6²)
= √(49 + 36)
= √85
≈ 9.22
Therefore, the length between the two points (2,4) and (-5,-2) is approximately 9.22 (rounded to the nearest hundredth).