The midpoint of \( \overline{J K} \) is \( M(13,6) \). One endpoint is \( J(17,10) \). Find the coordinates of the other endpoint \( K \). Write the coordinates as decimals or integers. Subrtyt

To find the coordinates of the other endpoint \( K(x, y) \), we can use the midpoint formula. The midpoint \( M \) of a line segment with endpoints \( J(x_1, y_1) \) and \( K(x_2, y_2) \) is given by: \[ M\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given \( M(13, 6) \) and \( J(17, 10) \), we have: - \( x_1 = 17 \), \( y_1 = 10 \) - \( M_x = 13 \), \( M_y = 6 \) Setting up the equations: 1. \( \frac{17 + x}{2} = 13 \) 2. \( \frac{10 + y}{2} = 6 \) Now, solving for \( x \): \[ \frac{17 + x}{2} = 13 \implies 17 + x = 26 \implies x = 26 - 17 \implies x = 9 \] Now, solving for \( y \): \[ \frac{10 + y}{2} = 6 \implies 10 + y = 12 \implies y = 12 - 10 \implies y = 2 \] Thus, the coordinates of the other endpoint \( K \) are \( (9, 2) \). So, the final answer is \( K(9, 2) \).