Final answer:
The coordinates of the midpoint of the segment with endpoints H(8,2) and K(6,10) are (7,6), obtained by averaging the corresponding x and y coordinates of H and K.
Step-by-step explanation:
To find the coordinates of the midpoint of the segment with endpoints H(8,2) and K(6,10), we need to use the midpoint formula. The midpoint formula is given by the average of the x-coordinates and the y-coordinates of the endpoints:
- Midpoint x-coordinate = (x₁ + x₂) / 2
- Midpoint y-coordinate = (y₁ + y₂) / 2
Plugging in the values from points H and K, we get:
- Midpoint x-coordinate = (8 + 6) / 2 = 14 / 2 = 7
- Midpoint y-coordinate = (2 + 10) / 2 = 12 / 2 = 6
Therefore, the coordinates of the midpoint are (7,6), which corresponds to option a. (7,6).