Final answer:
The midpoint between the points (4a, 5g) and (-6a, -g) is calculated by averaging the x-coordinates and y-coordinates separately. The correct midpoint is (-a, 2g), which corresponds to option A.
Step-by-step explanation:
The midpoint of a line segment between two points is found by averaging the x-coordinates and the y-coordinates of the endpoints. Let's find the midpoint for points (4a, 5g) and (-6a, -g). To calculate the midpoint (M), we use the formula: M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right. Let's plug in the values: M = \left(\frac{4a + (-6a)}{2}, \frac{5g + (-g)}{2}\right). Now, simplify: M = \left(\frac{-2a}{2}, \frac{4g}{2}\right). M = \left(-a, 2g\right. The midpoint is (-a, 2g), which corresponds to option A.