ind the coordinate of the other endpoint if the Midpoint is \( (-6,1) \) and one endpoint is \( (4,5) \) \[ \frac{\left(\frac{x 1+x_{2}}{2}\right.}{} \]

To find the other endpoint, we can use the midpoint formula. The midpoint \( M \) is given by the formula \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \). Given that \( M = (-6, 1) \) and one endpoint \( A(4, 5) \), we can set up the equations: \[ -6 = \frac{4 + x_2}{2} \quad \text{and} \quad 1 = \frac{5 + y_2}{2} \] From the first equation, multiplying through by 2 gives us \( -12 = 4 + x_2 \), leading to \( x_2 = -16 \). From the second equation, multiplying by 2 gives \( 2 = 5 + y_2 \), leading to \( y_2 = -3 \). Therefore, the other endpoint is \( (-16, -3) \). Additionally, using this formula can help you visualize points on a graph. The midpoint’s symmetrical nature means that if you were to plot both endpoints and the midpoint, you would see how they evenly divide the line segment, making it a handy tool in both geometry and coordinate systems. It's like finding the balance point on a seesaw! When using the midpoint formula, a common mistake is to forget to multiply the whole expression by 2 when working backwards. Always double-check your calculations! It’s easy to skip a step and end up with the wrong coordinates. So, take your time, and ensure each part is accurately calculated. It’s all about those little details!