Question

A circle with center D(0, -6) passes through the point C(5, -1). Use the Pythagorean Theorem to find the length of the circle’s radius, .

=

Answer 1

The radius of circle = 5√2 units

Explanation:

Points remember

Distance formula:-

Let (x₁, y₁) and (x₂, y₂) be the two points, then the distance between these two points is given by

Distance = √[(x₂ - x₁)² + (y - y₁)²]

It is given that, center of circle (0, -6) and passes through (5, -1)

To find the radius of circle

Here (x₁, y₁) = (0, -6) and (x₂, y₂) = (5, -1)

Radius r = √[(x₂ - x₁)² + (y - y₁)²]

= √[(5 - 0)² + (-1 - -6)²]

= √(5² + 5²) = √(25 + 25) = √50 = 5√2 units

Therefore radius of circle = 5√2 units

Answer 2

Length of radius =
`5√(2)`

Explanation:

The radius of the circle is the distance between the center and the point on the circle given.

The distance formula is
`√((y_2-y_1)^2+(x_2-x_1)^2)`

Where

x_1 = 0

y_1 = -6

and

x_2 = 5

y_2 = -1

plugging these into the formula we get:

`√((y_2-y_1)^2+(x_2-x_1)^2) \\=√((-1-(-6))^2+(5-0)^2) \\=√((-1+6)^2+(5)^2) \\=√(5^2 + 5^2) \\=√(50) \\=5√(2)`