In Figure, the ratio of $¯ ¯¯¯¯¯¯¯ ¯ D E$ to $¯ ¯¯¯¯¯¯ ¯ E F$ is 4 to 9. If $¯ ¯¯¯¯¯¯¯ ¯ D F = 2$ , calculate the distance from D to the midpoint of $¯ ¯¯¯¯¯¯ ¯ E F$ .

\frac{9}{13}

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\frac{12}{13}

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\frac{14}{13}

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\frac{16}{13}

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\frac{17}{13}

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Solution

The correct option is E $\frac{17}{13}$
Given $D F = 2$ , and ratio of $D E$ to $E F$ is $4$ to $9$
Therefore $D E = \frac{4}{13} \times 2 = \frac{8}{13}$ and $E F = \frac{9}{13} \times 2 = \frac{18}{13}$
distance from $D$ to the midpoint of $E F$ is $D E + E F / 2 = 8 / 13 + 9 / 13 = 17 / 13$

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In Figure, the ratio of ¯¯¯¯¯¯¯¯¯DE to ¯¯¯¯¯¯¯¯EF is 4 to 9. If ¯¯¯¯¯¯¯¯¯DF=2, calculate the distance from D to the midpoint of ¯¯¯¯¯¯¯¯EF.

The correct option is E 1713Given DF=2 , and ratio of DE to EF is 4 to 9Therefore DE=413×2=813 and EF=913×2=1813distance from D to the midpoint of EF is DE+EF/2=8/13+9/13=17/13

In Figure, the ratio of $¯ ¯¯¯¯¯¯¯ ¯ D E$ to $¯ ¯¯¯¯¯¯ ¯ E F$ is 4 to 9. If $¯ ¯¯¯¯¯¯¯ ¯ D F = 2$ , calculate the distance from D to the midpoint of $¯ ¯¯¯¯¯¯ ¯ E F$ .

The correct option is E $\frac{17}{13}$
Given $D F = 2$ , and ratio of $D E$ to $E F$ is $4$ to $9$
Therefore $D E = \frac{4}{13} \times 2 = \frac{8}{13}$ and $E F = \frac{9}{13} \times 2 = \frac{18}{13}$
distance from $D$ to the midpoint of $E F$ is $D E + E F / 2 = 8 / 13 + 9 / 13 = 17 / 13$