Find all points having an \( x \)-coordinate of 4 whose distance from the point \( (-2,-1) \) is 10 . The point(s) is(are) \( \square \). (Type an ordered pair. Use a comma to separate answers as needed.)

To find the points with an \( x \)-coordinate of 4 that are 10 units away from the point \( (-2, -1) \), we can use the distance formula. The distance \( D \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] In our case, we have: - \( (x_1, y_1) = (4, y) \) - \( (x_2, y_2) = (-2, -1) \) - \( D = 10 \) Plugging in the values, we get: \[ 10 = \sqrt{(4 - (-2))^2 + (y - (-1))^2} \] This simplifies to: \[ 10 = \sqrt{(4 + 2)^2 + (y + 1)^2} \] \[ 10 = \sqrt{6^2 + (y + 1)^2} \] \[ 10 = \sqrt{36 + (y + 1)^2} \] Now, squaring both sides: \[ 100 = 36 + (y + 1)^2 \] \[ 100 - 36 = (y + 1)^2 \] \[ 64 = (y + 1)^2 \] Taking the square root of both sides gives us: \[ y + 1 = 8 \quad \text{or} \quad y + 1 = -8 \] \[ y = 7 \quad \text{or} \quad y = -9 \] Thus, the points we found are: \[ (4, 7) \quad \text{and} \quad (4, -9) \] The point(s) is(are) \( (4, 7), (4, -9) \).