Question

The center of Circle D is (0,0). The circumference of the circle passes through Point E (-7,-4).
Find the length of the radius of Circle D.

Answer 1

Answer:

$\boxed{\sqrt{65}}$

Step-by-step explanation:

The radius of circle D is the distance from the origin to (-4, -7).

In math, the distance formula gives us the distance between two points, (x₁, y₁) and x₂, y₂):

$d = \sqrt{(x _{2}-x_{1})^{2} +(y _{2}-y_{1})^{2}}$

You are really using Pythagoras' Theorem to find the distance. You are building a right triangle whose hypotenuse connects two given points.  

For example, in the blue triangle below, the distance between the points (0,0) and (-4, -7) is

$d = \sqrt{(0 - (-4))^{2} +(0 -(- 7))^{2}}\\\\ = \sqrt{4^{2} +7^{2}}\\ = \sqrt{16 + 49}\\=\sqrt{65}$

$\text{The radius of the circle is }\boxed{\mathbf{\sqrt{65}}}$