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.