Question

a circle is centered at ( i(0,0) ). the point ( t(3,4) ) is on the circle.
where does the point ( z(-sqrt{13},sqrt{74}) ) lie?
choose 1 answer
inside the circle
on the circle
outside the circle

Explanation:

Step1: Calculate the radius of the circle

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For the center \(I(0,0)\) and the point \(T(3,4)\) on the circle, the radius \(r=\sqrt{(3 - 0)^2+(4 - 0)^2}=\sqrt{9 + 16}=\sqrt{25}=5\).

Step2: Calculate the distance from the center to point \(Z(-\sqrt{13},\sqrt{74})\)

Using the distance formula, \(d=\sqrt{(-\sqrt{13}-0)^2+(\sqrt{74}-0)^2}=\sqrt{13 + 74}=\sqrt{87}\approx9.33\).

Answer:

C. Outside the circle