1. The problem asks to find all points that are the same distance from Point A as Point B is from Point A. 2. First, identify the coordinates of Point A and Point B. Point A is at $(-1,0)$. Point B is at $(-3,-2)$. 3. Calculate the distance between Point A and Point B using the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ Substitute $x_1 = -1$, $y_1 = 0$, $x_2 = -3$, $y_2 = -2$: $$d = \sqrt{(-3 + 1)^2 + (-2 - 0)^2} = \sqrt{(-2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$$ 4. We want to find all points $(x,y)$ such that the distance from Point A $(-1,0)$ to $(x,y)$ is also $2\sqrt{2}$. Using the distance formula: $$\sqrt{(x + 1)^2 + (y - 0)^2} = 2\sqrt{2}$$ 5. Square both sides to eliminate the square root: $$(x + 1)^2 + y^2 = (2\sqrt{2})^2 = 8$$ 6. This equation represents a circle centered at $(-1,0)$ with radius $2\sqrt{2}$. 7. Check each given point to see if it satisfies the equation: - $(0, -2)$: $(0 + 1)^2 + (-2)^2 = 1^2 + 4 = 1 + 4 = 5 \neq 8$ - $(-4, -2)$: $(-4 + 1)^2 + (-2)^2 = (-3)^2 + 4 = 9 + 4 = 13 \neq 8$ - $(-4, 0)$: $(-4 + 1)^2 + 0^2 = (-3)^2 + 0 = 9 + 0 = 9 \neq 8$ - $(-2, 2)$: $(-2 + 1)^2 + 2^2 = (-1)^2 + 4 = 1 + 4 = 5 \neq 8$ - $(0, 0)$: $(0 + 1)^2 + 0^2 = 1^2 + 0 = 1 + 0 = 1 \neq 8$ 8. None of the points satisfy the exact distance $2\sqrt{2}$ from Point A. 9. However, since the problem asks to select all points the same distance from Point A as Point B, and none of the given points satisfy the distance exactly, the answer is that none of the listed points are the same distance from Point A as Point B. Final answer: No points from the given list are the same distance from Point A as Point B.