To find the values of a and b, we can use the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.
Let's break it down step by step:
1. The x-coordinate of point A is -3, and the x-coordinate of point B is 47. To find the x-coordinate of the midpoint, we take the average of -3 and 47: (-3 + 47) / 2 = 44 / 2 = 22. So, the x-coordinate of the midpoint is 22.
2. The y-coordinate of point A is 11, and the y-coordinate of the midpoint is -79. To find the y-coordinate of the midpoint, we take the average of 11 and -79: (11 + (-79)) / 2 = -68 / 2 = -34. So, the y-coordinate of the midpoint is -34.
Therefore, the values of a and b are a = 22 and b = -34, respectively.