Question

Apply the Pythagorean Theorem to find the length between (2, -3)  and (5, 5) . Round to nearest hundredth if needed

Answer 1

To find the length between the points (2, -3) and (5, 5) using the Pythagorean Theorem, we can consider the distance between the x-coordinates and the distance between the y-coordinates as the two sides of a right triangle.

The distance between the x-coordinates is 5 - 2 = 3.
The distance between the y-coordinates is 5 - (-3) = 8.

Using the Pythagorean Theorem, where c represents the hypotenuse of the right triangle (the distance between the two points), we have:

c² = a² + b²,

where:
a = 3 (distance between the x-coordinates)
b = 8 (distance between the y-coordinates)

Plugging in these values, we get:

c² = 3² + 8²
c² = 9 + 64
c² = 73

Taking the square root of both sides, we find:

c = √73 ≈ 8.54 (rounded to the nearest hundredth)

Therefore, the length between the points (2, -3) and (5, 5) is approximately 8.54 units.