Question

Which of these points lies on the circle with the center (2,3) and radius 2?

Answer 1

Answer:

A. (4, 3)

Step-by-step explanation:

If the point (x, y) lies on a circle, then the distance between this point and the center is equal to the radius.

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have the center in (2, 3) and the radius r = 2.

Check for

$A.\ (4,\ 3)\\\\d=\sqrt{(4-2)^2+(3-3)^2}=\sqrt{2^2+0^2}=\sqrt{4+0}=\sqrt4=2\\\\\bold{CORRECT}\\\\B.\ (-1,\ 0)\\\\d=\sqrt{(-1-2)^2+(0-3)^2}=\sqrt{(-3)^2+(-3)^2}=\sqrt{9+9}=\sqrt{18}\neq2\\\\C.\ (1,\ 3)\\\\d=\sqrt{(1-2)^2+(3-3)^2}=\sqrt{(-1)^2+0^2}=\sqrt{1+0}=\sqrt{1}=1\neq2\\\\D.\ (3,\ 4)\\\\d=\sqrt{(3-2)^2+(4-3)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt2\neq2$

Answer 2

Answer:

The answer to your question is the letter A.

Step-by-step explanation:

Data

Center = (2, 3)

radius = 2

Process

1.- Find the equation of the line

              (x - h)² + (y - k)² = r²

-Substitution

              (x - 2)² + (y - 3)² = 2²  

-Simplification

              (x - 2)² + (y - 3)² = 4

-Evaluate the points in the equation

A. (4, 3)

              (4 - 2)² + (3 - 3)² = 4

                   2² + 0 = 4

                           4 = 4     This point lies in the circle

B (-1, 0)

              (-1 - 2)² + (0 - 3)² = 4

                        -3² + (-3)² = 4

                          9 + 9 = 4   This point is not part of the circle

C. (1, 3)

              (1 - 2)² + (3 - 3)² = 4

                 (-1)² + (0)² = 4

                            1 = 4          This point is not part of the circle

D. (3, 4)

              (3 - 2)² + (4 - 3)² = 4

                     1² + 1² = 4

                            2 = 4          This point is not part of the circle