Final answer:
To find the length of segment MF when M is the midpoint of CF, calculate the midpoint's coordinates and then apply the distance formula to find the distance between the midpoint and point F which results in MF being the square root of 18.
Step-by-step explanation:
The student is asking how to find the length of the segment MF given that M is the midpoint of CF and the coordinates of C and F.
To find the midpoint M of CF, one must average the x-coordinates of C and F and the y-coordinates of C and F. Given point C (3, 1) and point F (9, 7), the midpoint M will have coordinates ((3+9)/2, (1+7)/2) which results in M (6, 4). The length of segment MF (MF) is equal to the distance from M to F.
Using the distance formula d = √((x2 - x1)^2 + (y2 - y1)^2), we calculate MF by subtracting the coordinates of M from F and then applying the formula which yields MF = √((9 - 6)^2 + (7 - 4)^2) = √(3^2 + 3^2) = √(9 + 9) = √18.