To determine which point lies on circle W, we need to calculate the distance from each point to the center of the circle W (-4, 6) and compare it to the radius of the circle.
The formula to calculate the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Let's calculate the distances from each point to the center of circle W:
For point A(0, 4):
\[ d_A = \sqrt{(0 - (-4))^2 + (4 - 6)^2} = \sqrt{16 + 4} = \sqrt{20} \approx 4.47 \]
For point B(2, 10):
\[ d_B = \sqrt{(2 - (-4))^2 + (10 - 6)^2} = \sqrt{36 + 16} = \sqrt{52} \approx 7.21 \]
For point C(4, 0):
\[ d_C = \sqrt{(4 - (-4))^2 + (0 - 6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \]
For point D(6, 16):
\[ d_D = \sqrt{(6 - (-4))^2 + (16 - 6)^2} = \sqrt{100 + 100} = \sqrt{200} \approx 14.14 \]
Comparing each distance to the radius of the circle (10 units):
- Point A: \(d_A \approx 4.47\)
- Point B: \(d_B \approx 7.21\)
- Point C: \(d_C = 10\) (on the circle)
- Point D: \(d_D \approx 14.14\)
Therefore, only point C(4, 0) lies on circle W.
Hope this helps!
