Question

the center of circle a is at (4,4), with a radius of 3. what should negins first step be to prove that the point b(7,4) lies on the circle?
(1 point)
negin should calculate the area of the circle.
negin should calculate the circumference of the circle.
negin should approximate the distance from a to b.
negin should use the distance formula to calculate the length of segment ab.

Explanation:

To prove if point \( B(7, 4) \) lies on circle \( A \) with center \( A(4, 4) \) and radius \( 3 \), we need to check if the distance between \( A \) and \( B \) is equal to the radius. The distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) is used to find the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\). So the first step is to calculate the distance from \( A \) to \( B \) using the distance formula. Among the options, the correct one is the one where Negin uses the distance formula to calculate the length of segment \( AB \) (or calculate the distance from \( A \) to \( B \), but the option "Negin should use the distance formula to calculate the length of segment \( AB \)" is more precise as we need an exact calculation, not an approximation).

Answer:

The correct option is: Negin should use the distance formula to calculate the length of segment \( AB \) (the last option with the radio button not selected in the image, but based on the analysis, it's the option stating "Negin should use the distance formula to calculate the length of segment \( AB \)"). If we consider the options as:

A. Negin should calculate the area of the circle.

B. Negin should calculate the circumference of the circle.

C. Negin should approximate the distance from \( A \) to \( B \).

D. Negin should use the distance formula to calculate the length of segment \( AB \).

Then the answer is D. Negin should use the distance formula to calculate the length of segment \( AB \)