Question

The point (5,4) lies on a circle. What is the length of the radius of

Answer 1

Answer:

$\large\boxed{r=2\sqrt2}$

Step-by-step explanation:

The radius (r) length is equal to the distance between the center of the circle and the point on the circle.

The formula of a distance:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the coordinates of the given points (5, 4) and (3, 2):

$r=\sqrt{(3-5)^2+(2-4)^2}\\\\r=\sqrt{(-2)^2+(-2)^2}\\\\r=\sqrt{4+4}\\\\r=\sqrt{(4)(2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\r=\sqrt4\cdot\sqrt2\\\\\boxed{r=2\sqrt2}$