A line segment is bisected by a line with the equation # 4 y + x = 3 #. If one end of the line segment is at #(5 ,6 )#, where is the other end?
1 Answer
The other end is at
Explanation:
Given the equation of the perpendicular bisector of the form:
The equation of the bisected line is of the form:
Writing the equation of the given perpendicular bisector in the above form:
Now, we can with the general form for the bisected line:
To find the value of
The equation of the bisected line is:
Find the point of intersection of the lines:
Multiply the second equation by 4 and add to the first equation:
Solve for x:
Use the given line to solve for y:
We can use the midpoint equations to find the other end:
Substitute
Solve for
The other end is at