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: Analyze the right - triangle in the circle

In a circle with center \(D(h,k)\) and a point \(E(x,y)\) on the circle, the right - triangle is formed with the radius \(r\) as the hypotenuse. The horizontal side length of the right - triangle is the difference in the \(x\) - coordinates of the center and the point on the circle, which is \(|x - h|\). The vertical side length of the right - triangle is the difference in the \(y\) - coordinates of the center and the point on the circle, which is \(|y - k|\).

Answer:

D. \(x - h\), G. \(y - k\)