Final answer:
To find the length of MF, the distance formula is used after calculating the midpoint M of CF with coordinates C(3,7) and F(5,5), resulting in MF being √2 units.
Step-by-step explanation:
The question asks to find the distance MF, where M is the midpoint of segment CF given the coordinates of the points C(3,7) and F(5,5). To find the coordinates of M, we need to use the midpoint formula:
Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)
Using the given points C(3,7) and F(5,5), we get:
M = ((3 + 5)/2, (7 + 5)/2) = (4, 6)
Now, we will use the distance formula to calculate MF:
Distance formula: D = √((x2 - x1)² + (y2 - y1)²)
Since M(4,6) and F(5,5) are the points in question, plugging in these values yields:
MF = √((5 - 4)² + (5 - 6)²) = √((1)² + (-1)²) = √(1 + 1) = √2
So, the length of segment MF is √2 units.