Final answer:
The midpoint of line segment HX with H(4 1/2, -4 3/4) and X(2 1/4, -1 3/4) is (3 3/8, -3 1/4).
Step-by-step explanation:
To find the midpoint of the line segment HX with H(4 1/2, -4 3/4) and X(2 1/4, -1 3/4), we first convert the mixed numbers into improper fractions for easier calculation:
- H becomes (9/2, -19/4)
- X becomes (9/4, -7/4)
Next, we use the midpoint formula, which is:
( (x1 + x2)/2, (y1 + y2)/2 )
Substituting the coordinates of H and X into the formula gives us the midpoint M:
M = ( (9/2 + 9/4)/2, (-19/4 + -7/4)/2 )
Combine like terms and simplify:
- x-coordinate: (18/4 + 9/4)/2 = 27/4 * 1/2 = 27/8 = 3 3/8
- y-coordinate: (-19/4 + -7/4)/2 = -26/4 * 1/2 = -26/8 = -3 1/4
Therefore, the midpoint M is (3 3/8, -3 1/4).