Final Answer:
c. 10
Step-by-step explanation:
M is the midpoint of CF, and to find the midpoint of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\), you can use the midpoint formula:
\[ M = \left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right) \]
For the given points C(5, 10) and F(7, 4), the midpoint M can be calculated as follows:
\[ M_x = \frac{{5 + 7}}{2} = 6 \]
\[ M_y = \frac{{10 + 4}}{2} = 7 \]
So, the midpoint M is (6, 7). Now, to find the distance between M and F, you can use the distance formula:
\[ d = \sqrt{{(x_2 - x_1)^2 + (y_2 - y_1)^2}} \]
Substituting the values for M(6, 7) and F(7, 4) into the formula:
\[ MF = \sqrt{{(7 - 6)^2 + (4 - 7)^2}} \]
\[ MF = \sqrt{{1^2 + (-3)^2}} \]
\[ MF = \sqrt{{1 + 9}} \]
\[ MF = \sqrt{{10}} \]
\[ MF = 10 \]
Therefore, the distance MF is 10, and the correct answer is option c.