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, the points (2, 5) and (7, 3) form the two sides of a right triangle, and we want to find the length of the hypotenuse.
First, we calculate the length of the horizontal side of the triangle:
7 - 2 = 5
Next, we calculate the length of the vertical side of the triangle:
3 - 5 = -2
Since we need to find the length, we take the absolute value of -2:
|-2| = 2
Now, we use the Pythagorean Theorem to find the length of the hypotenuse:
hypotenuse^2 = (horizontal side)^2 + (vertical side)^2
hypotenuse^2 = 5^2 + 2^2
hypotenuse^2 = 25 + 4
hypotenuse^2 = 29
To find the length of the hypotenuse, we take the square root of both sides:
hypotenuse = √29 ≈ 5.385
Rounded to the nearest hundredth, the length between (2, 5) and (7, 3) is approximately 5.38.
The answer is a. 5.38.