Final answer:
The midpoint M between points G(1,7) and H(-3,11) is M(-1, 9). The distance between G and H is approximately 5.66 units.
Step-by-step explanation:
The question asks for the coordinates of the midpoint M of the line segment with endpoints G(1,7) and H(-3,11), as well as the distance between these two endpoints. To find the midpoint of a line segment, we use the formula ( (x1+x2)/2 , (y1+y2)/2 ) where (x1, y1) and (x2, y2) are the coordinates of the endpoints. Here, the midpoint would be M( (1-3)/2, (7+11)/2 ) which simplifies to M(-1, 9).
To calculate the distance between the two points, we use the distance formula sqrt( (x2-x1)² + (y2-y1)² ). Plugging in the coordinates of G and H, the distance comes out to be sqrt( (-3-1)² + (11-7)² ) which simplifies to sqrt(4² + 4²), which is sqrt(32), or approximately 5.66.