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 horizontal side

The horizontal side of the right - triangle is the difference between the \(x\) - coordinates of points \(E(x,y)\) and \(D(h,k)\). Using the formula for the distance between two points on a horizontal line \(d=\vert x_2 - x_1\vert\), here \(x_2=x\) and \(x_1 = h\), so the length is \(|x - h|\).

Step2: Analyze the vertical side

The vertical side of the right - triangle is the difference between the \(y\) - coordinates of points \(E(x,y)\) and \(D(h,k)\). Using the formula for the distance between two points on a vertical line \(d=\vert y_2 - y_1\vert\), here \(y_2=y\) and \(y_1 = k\), so the length is \(|y - k|\).

Answer:

\(x - h\), \(y - k\)