Apply the Pythagorean Theorem to find the length between (2, 5)
and (7, 3)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses
4.58
4.58
2.65
2.65
5.39
5.39
29
The length between (2, 5) and (7, 3) can be found using the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's label the points as follows:
Point 1: (x1, y1) = (2, 5)
Point 2: (x2, y2) = (7, 3)
The length between these two points can be found using the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
So, plugging in the values:
d = √((7 - 2)^2 + (3 - 5)^2)
d = √(5^2 + (-2)^2)
d = √(25 + 4)
d = √29
d ≈ 5.39
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39.