Final answer:
To find point H which, together with point A, flanks midpoint K, we apply the midpoint formula to each coordinate, resulting in H being located at (7, 1).
Step-by-step explanation:
The question involves finding the coordinates of a point H that forms a segment with given points A and K. In this case, K is the midpoint between points A and H. Since we have the coordinates for point A (5, -7) and the midpoint K (6, -3), we can find point H by using the midpoint formula, which states that the coordinates of the midpoint are the average of the coordinates of the endpoints. To find H, we need to set up two equations to find the x and y coordinates separately.
To find the x-coordinate of H, we use the formula: (xA + xH) / 2 = xK. Plugging in our known values we get (5 + xH) / 2 = 6. Solving for xH, we find that xH = 7. Similarly, to find the y-coordinate of H, we use the formula: (yA + yH) / 2 = yK. Using the known values we get (-7 + yH) / 2 = -3. Solving for yH, we find that yH = 1. Therefore, the coordinates of point H are (7, 1).