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Prove that the mid-point of the hypoten...

Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices.

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To prove that the midpoint of the hypotenuse of a right-angled triangle is equidistant from its vertices, we can follow these steps: ### Step 1: Define the Triangle and Midpoint Let triangle ABC be a right-angled triangle with the right angle at vertex B. Let D be the midpoint of the hypotenuse AC. ### Step 2: Use the Midpoint Formula Since D is the midpoint of AC, we can express the coordinates of D in terms of A and C. If A has coordinates (x1, y1) and C has coordinates (x2, y2), then the coordinates of D are given by: \[ D\left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right) \] ...
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