Given:
AB is the diameter of a circle whose center is the point (4,-3).
Coordinates of A are (-1,5).
To find:
The measure of AB.
Solution:
Let point O(4,-3) be the center of the circle.
Then, OA is the radius of the circle.
We know that, diameter of a circle is twice of its radius.
So, [tex]AB=2(OA)[/tex] ...(i)
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, the distance between O and A is
[tex]OA=\sqrt{(-1-4)^2+(5-(-3))^2}[/tex]
[tex]OA=\sqrt{(-5)^2+(5+3)^2}[/tex]
[tex]OA=\sqrt{25+(8)^2}[/tex]
[tex]OA=\sqrt{25+64}[/tex]
[tex]OA=\sqrt{89}[/tex]
Now, using (i), we get
[tex]AB=2(OA)[/tex]
[tex]AB=2(\sqrt{89})[/tex]
[tex]AB=2\sqrt{89}[/tex]
Therefore, the measure of AB is [tex]2\sqrt{89}[/tex] units.
