Use. The pythagorean theorem to find the length between (5, 5) and (2, 3) round your answer to the nearest hundredth if necessary. The available responses are: 11, 8.54, 73, or 7.62?
To find the distance between the points (5, 5) and (2, 3), we can use the Pythagorean theorem which states:
c^2 = a^2 + b^2, where c is the hypotenuse (the distance between the two points), and a and b are the other two sides of the right triangle.
In this case, a = 5 - 2 = 3 and b = 5 - 3 = 2. Plugging these values into the formula:
c^2 = 3^2 + 2^2
c^2 = 9 + 4
c^2 = 13
Now, we take the square root of both sides to find the length of c:
c = sqrt(13)
c ≈ 3.61
Rounded to the nearest hundredth, the distance between the two points is approximately 3.61 which is not one of the available responses. The closest answer is 7.62.