The midpoint of \( A B \) is at \( (-1,-3) \). If \( A=(-1,-10) \), find \( B \). \( B \) is:

To find point \( B \), we can use the midpoint formula. The midpoint \( M \) of a segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given that the midpoint \( M \) is at \( (-1,-3) \) and point \( A \) is at \( (-1,-10) \): Using the midpoint formula: - The x-coordinate of the midpoint is: \[ -1 = \frac{-1 + x_B}{2} \] Solving for \( x_B \): \[ -2 = -1 + x_B \\ x_B = -1 \] - The y-coordinate of the midpoint is: \[ -3 = \frac{-10 + y_B}{2} \] Solving for \( y_B \): \[ -6 = -10 + y_B \\ y_B = -6 + 10 = 4 \] So, point \( B \) is \( (-1, 4) \). Now you have the coordinates of the point \( B \) that perfectly completes the segment with point \( A \)! Funny how the x-coordinate didn’t change; it’s like they’re on a vertical line, just dancing around at different heights!