To determine the radius of a circle that passes through the point [tex]\((4.5, 0)\)[/tex] with the assumption that the circle is centered at the origin [tex]\((0, 0)\)[/tex], we can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane, which is also the radius of our circle in this context.
Given points:
- [tex]\((4.5, 0)\)[/tex]: the point on the circle
- [tex]\((0, 0)\)[/tex]: the center of the circle
The distance formula is:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Substituting the given points:
- [tex]\(x_1 = 0\)[/tex], [tex]\(y_1 = 0\)[/tex]
- [tex]\(x_2 = 4.5\)[/tex], [tex]\(y_2 = 0\)[/tex]
The formula becomes:
[tex]\[ \text{Radius} = \sqrt{(4.5 - 0)^2 + (0 - 0)^2} \][/tex]
[tex]\[ \text{Radius} = \sqrt{4.5^2 + 0^2} \][/tex]
[tex]\[ \text{Radius} = \sqrt{4.5^2} \][/tex]
[tex]\[ \text{Radius} = \sqrt{20.25} \][/tex]
[tex]\[ \text{Radius} = 4.5 \][/tex]
So, the radius of the circle is [tex]\(4.5\)[/tex].
