Question

Consider a circle centered at (-2,3), where point A(2,3) is on the circle. Which of the following points would also be on the circle?

Answer 1

Without the specific options to choose from, it's not possible to directly identify additional points on the circle, but any point that lies 4 units away from the center at (-2,3) in any direction would be on the circle.

Step-by-step explanation:

The subject of this question is Mathematics, and it appears to be at the High School level. To find additional points on the circle, we would need to use the radius of the circle. Since point A(2,3) lies on the circle and the center of the circle is at (-2,3), the radius is the distance between these points. Using the distance formula, √((x2-x1)²+(y2-y1)²), the radius is √((2-(-2))²+(3-3)²) = √(4²+0²) = 4.

Any point (x, y) that also satisfies the equation (x - (-2))² + (y - 3)² = 4² will be on the circle. Without the specific options to choose from, we cannot determine which of the given points would also be on the circle. However, we can say that such a point would have to be exactly 4 units away from the center, at (-2,3), following the circle's equation.

Answer 2

The point that could also be on the circle is (-6, 3)

Which point could also be on the circle?

From the question, we have the following parameters that can be used in our computation:

Center = (-2, 3)

Point = (2, 3)

The equation of a circle is represented as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

So, we have

(x + 2)² + (y - 3)² = r²

Using the point (2, 3), we have

(2 + 2)² + (3 - 3)² = r²

16 = r²

So, we have

(x + 2)² + (y - 3)² = 16

From the list of options, we have

(-6, 3)

Testing this option, we have

(-6 + 2)² + (3 - 3)² = 16

Evaluate

16 = 16

This equation is true

Hence, the point that could also be on the circle is (-6, 3)

Question

Consider a circle centered at (-2,3), where point A(2,3) is on the circle. Which of the following points would also be on the circle?

(-2, -2)

(-2, 8)

(-6, 3)

(6, -3)