# A line segment is bisected by a line with the equation # 5 y -4 x = 1 #. If one end of the line segment is at #(3 ,4 )#, where is the other end?

##### 1 Answer

The other end is

#### Explanation:

Let's rewrite the equation of the line

The slope is

The slope of a line perpendicular is

as

The equation of the segment is

The point of intersection of the lines

The point of intersection is

Let the other end of the segment be

Then,

and

The other end is

graph{(y-4/5x-1/5)(y+5/4x-31/4)((x-3)^2+(y-4)^2-0.01)((x-179/41)^2+(y-94/41)^2-0.01)=0 [-1.985, 9.116, -0.99, 4.56]}