Questions: Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x, y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.) midpoint (15,-23), endpoint (9,-19) The other endpoint is

To find the coordinates of the other endpoint of a line segment given its midpoint and one endpoint, we can use the midpoint formula. The midpoint formula states that the midpoint \( M(x_m, y_m) \) of a segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:

\[ x_m = \frac{x_1 + x_2}{2} \] \[ y_m = \frac{y_1 + y_2}{2} \]

Given the midpoint and one endpoint, we can set up equations to solve for the unknown coordinates of the other endpoint.

1. Use the midpoint formula to set up equations for the x and y coordinates.
2. Solve these equations to find the unknown coordinates of the other endpoint.

Se nos da el punto medio \( M(15, -23) \) y un extremo del segmento \( A(9, -19) \). Queremos encontrar las coordenadas del otro extremo \( B(x_2, y_2) \).

La fórmula del punto medio establece que:

\[ x_m = \frac{x_1 + x_2}{2} \] \[ y_m = \frac{y_1 + y_2}{2} \]

Sustituyendo los valores conocidos:

\[ 15 = \frac{9 + x_2}{2} \] \[ -23 = \frac{-19 + y_2}{2} \]

Multiplicamos ambas ecuaciones por 2 para despejar \( x_2 \) y \( y_2 \):

1. Para \( x_2 \): \[ 30 = 9 + x_2 \implies x_2 = 30 - 9 = 21 \]

2. Para \( y_2 \): \[ -46 = -19 + y_2 \implies y_2 = -46 + 19 = -27 \]

Las coordenadas del otro extremo \( B \) son \( (21, -27) \).

\(\boxed{(21, -27)}\)