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

`\boxed{√(65)}`

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)}\\ = √(16 + 49)\\=√(65)`

`\text{The radius of the circle is }\boxed{\mathbf{√(65)}}`