Question

Does the point (1, √7) lie on the circle shown? Explain.

1) Yes, the distance from (-2, 4) to (1, √7) is 4 units.
2) Yes, the distance from (-2, 0) to (1, √7) is 4 units.
3) No, the distance from (-2, 0) to (1, √7) is not 4 units.
4) No, the distance from (-2, 4) to (1, √7) is not 4 units.

Answer 1

The point (1, √7) does not lie on the circle shown because the distance from the center of the circle to the given point is not 4 units.

Step-by-step explanation:

To determine whether the point (1, √7) lies on the circle, we need to find the distance from the center of the circle to the given point. The center of the circle is (-2, 4).

Using the distance formula, we can calculate the distance between (-2, 4) and (1, √7). The formula is d = √((x2 - x1)^2 + (y2 - y1)^2).

Plugging in the coordinates, we get d = √((1 - (-2))^2 + (√7 - 4)^2) = √(3^2 + (√7 - 4)^2) = √(9 + 7 - 8√7 + 16) = √(32 - 8√7).

The distance, √(32 - 8√7), is not equal to 4 units. Therefore, the correct answer is option 4) No, the distance from (-2, 4) to (1, √7) is not 4 units.