#1**+2 **

Coordinate Geometry may be useful in this. (the following graph is not to scale)

Find slope of line FB

So we find the rise and run of EB

The rise is 7, and the run is 5.

So the slope of FB is \(-\frac{7}{5}\)

We know that the line FB intersects the x-axis, so the x-intercept is (7,0)

We have the equation \(y=-\frac{7}{5}x+b\). Finding the y intercept will help us find the length of DF

We solve for b by plugging in (7,0) into our above equation. 0=-(7/5)*7+b = b=(49/5)

So the y intercept is (0, 9.8)

That means that AF = 9.8, and since AD is 7,

9.8 - 7 = 2.8

\(\boxed{DF\text{ is } 2.8}\)

.CalculatorUser Oct 13, 2019