Question
Apply the Pythagorean Theorem to find the length Between (2,5) and (7,3). Round your answers to the nearest hundredth if necessary.
Answers
Answered by
GPT 3.5
To apply the Pythagorean Theorem to find the length between the points (2,5) and (7,3), we need to find the distance between the x-coordinates and the distance between the y-coordinates.
The distance between the x-coordinates is calculated by subtracting the x-coordinate of one point from the x-coordinate of the other point:
7 - 2 = 5
Similarly, the distance between the y-coordinates is calculated by subtracting the y-coordinate of one point from the y-coordinate of the other point:
3 - 5 = -2
Now, we can use these distances to find the length between the two points by applying the Pythagorean Theorem:
Length = √((distance between x-coordinates)^2 + (distance between y-coordinates)^2)
= √(5^2 + (-2)^2)
= √(25 + 4)
= √29
Since we are asked to round the answer to the nearest hundredth, the length between the given points is approximately 5.39.
The distance between the x-coordinates is calculated by subtracting the x-coordinate of one point from the x-coordinate of the other point:
7 - 2 = 5
Similarly, the distance between the y-coordinates is calculated by subtracting the y-coordinate of one point from the y-coordinate of the other point:
3 - 5 = -2
Now, we can use these distances to find the length between the two points by applying the Pythagorean Theorem:
Length = √((distance between x-coordinates)^2 + (distance between y-coordinates)^2)
= √(5^2 + (-2)^2)
= √(25 + 4)
= √29
Since we are asked to round the answer to the nearest hundredth, the length between the given points is approximately 5.39.