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If M is the midpoint of CF, then the length of MF is half the length of CF.

[tex]C(3,4) \\ x_1=3 \\ y_1=4 \\ \\ F(9,8) \\ x_2=9 \\ y_2=8 \\ \\ \overline{CF}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(9-3)^2+(8-4)^2}= \\ =\sqrt{6^2+4^2}=\sqrt{36+16}=\sqrt{4(9+4)}=\sqrt{4 \times 13}=2\sqrt{13} \\ \\ \overline{MF}=\frac{\overline{CF}}{2}=\frac{2\sqrt{13}}{2}=\sqrt{13}[/tex]

The length of MF is √13 units.
Louli

Answer:

MF = √13 units


Explanation:

1- We get the distance between C and F:

The distance formula is as follows:

distance = [tex] \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} [/tex]

We have:

point C (3,4) and point F (9,8)

This means that:

CF = [tex] \sqrt{(8-4)^2+(9-3)^2} [/tex]

CF = 2√13 units


2- We get MF:

We know that M is the midpoint of CF, this means that:

CM = MF

and

CM + MF = CF

Therefore:

MF would be equal to half CF

MF = 0.5 * 2√13 = √13 units


Hope this helps :)

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