A line segment is bisected by a line with the equation # 4 y - 6 x = 8 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?
1 Answer
Explanation:
First rearrange
This will be perpendicular to the line through the point
We need to find the equation of this line. We know that if two lines are perpendicular then the product of their gradients is
Gradient of
Let
Then:
Using point slope form of a line and point
The intersection of
Substitute in
Co-ordinates of midpoint
The co-ordinates of the midpoint are given by:
So:
If the end points are
We have
Hence:
and
So other end point is: