# A line segment is bisected by a line with the equation # -7 y + 5 x = 1 #. If one end of the line segment is at #(1 ,4 )#, where is the other end?

##### 1 Answer

I get

#### Explanation:

I find it less confusing this way:

The perpendicular family is gotten by swapping the coefficients on

We find the meet by multiplying the first by 5 and the second by 7:

Adding,

If we call our endpoint E and our meet M we get an informal equation for the other endpoint F that's

So our other endpoint is

Check:

Let's see if we can get the grapher to graph it:

graph{ ( -7 y + 5x - 1) ( (y-4)(157/37 -1) - (x-1)( -20/37 -4 ) ) = 0 [-7.83, 12.17, -2.44, 7.56]}

Looks pretty good.