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In the diagram, $E$ is the midpoint of line $DG$ and $F$ is the midpoint of line $EG$ . The coordinates of $F$ are:

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(8, 3)

(6, 3)

(6, 2)

(7, 3)

answer is C.

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Detailed Solution

Given,

E

is the midpoint of line

DG

and

F

is the midpoint of line

EG

Let the coordinate of G be (a,b) & F be (x,y)
As E is mid lot of OG,
Midpoint of two point

{(x}_{1}, y_{1})

{(x}_{2}, y_{2})

is ,

(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

\Rightarrow (\frac{a + 1}{2}, \frac{b + 6}{2}) = (5, 4)

Equating x and y-coordinates, we get,

\Rightarrow \frac{a + 1}{2} = 5 and \frac{b + 6}{2} = 4

\Rightarrow a + 1 = 10 and b + 6 = 8

\Rightarrow a = 9 and b = 2

\Rightarrow (a, b) = (9, 2)

As F is midpoint of EG,

\Rightarrow (x, y) = (\frac{5 + 9}{2}, \frac{4 + 2}{2})

\Rightarrow (x, y) = (7, 3)

Thus, the coordinates of F are (7,3).
Therefore, option (3) is correct.

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