A line segment is bisected by a line with the equation # - 4 y + x = 1 #. If one end of the line segment is at #( 7 , 2 )#, where is the other end?
1 Answer
The other end is at
Explanation:
Let's write the given line in the form
The general equation of lines perpendicular to this line is:
To find the value of c, substitute 7 for x and 2 for y:
The equation of the bisected line segment is:
The midpoint is at the intersection of of these two lines:
Multiply equation [1] by 4 and subtract from equation [2]
Let
The y coordinate of the other end of the line,
To find the corresponding x coordinate, substitute
The other end is at
Here is a graph of two lines and two points: