Question

to derive the standard formula of a circle, a radius r is constructed as the hypotenuse of a right triangle as shown. what are the lengths of the sides of the right triangle that is formed? check all that apply. h k h - k x - h x - y y - h y - k

Explanation:

Step1: Recall distance in coordinate - geometry

The horizontal distance between two points \(D(h,k)\) and \(E(x,y)\) is given by the difference in their \(x\) - coordinates. The vertical distance is given by the difference in their \(y\) - coordinates.

Step2: Determine the sides of the right - triangle

In a right - triangle formed with the center \(D(h,k)\) and a point on the circle \(E(x,y)\), the horizontal side length is \(|x - h|\) and the vertical side length is \(|y - k|\).

Answer:

x - h, y - k