To solve the problem of finding the distance between two points (or the hypotenuse of a right triangle), we use the distance formula derived from the Pythagorean theorem. Here's the step-by-step approach:

Step 1: Identify the coordinates of the two points

Let the points be (A(x_1, y_1)) and (B(x_2, y_2)). For example, if the points are ((3,0)) and ((0,4)):
(x_1=3, y_1=0) and (x_2=0, y_2=4).

Step 2: Calculate differences in coordinates

• Horizontal difference: (\Delta x = x_2 - x_1 = 0-3 = -3)
• Vertical difference: (\Delta y = y_2 - y_1 =4-0=4)

Step3: Apply the distance formula

[d = \sqrt{(\Delta x)^2 + (\Delta y)^2}]
Substitute values:
[d = \sqrt{(-3)^2 + 4^2} = \sqrt{9+16} = \sqrt{25}=5]

Answer: (\boxed{5}) (assuming the example points; adjust based on actual coordinates in the image, but this is a common result).

(\boxed{5})

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