Question 1204346
Equation of line the line through points of(-5,2) and g(3,4)
use formula 

(y-y1)/(y1-y2) = (x-x1)/(x1-x2)
we get

2x - 8y + 26 = 0.....................................(1)


Slope of of line the line through points of(-5,2) and g(3,4)

(y1-y2)/(x1-x2)  we get m=1/4

A perpendicular line to fg will have slope -4

Equation of line the line through point(1,-4) m=-4

y=-4x

substitute y in (1)
solve

we get

(-13/17, 52/17)

Distance between (-13/17, 52/17) and (1,-4)

7.06 units The perpendicular distance from E to the line

 *[illustration distance.png].