A line segment is bisected by a line with the equation # 2 y + 3 x = 3 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?
1 Answer
To other end is at the point
Explanation:
The equation of any line segment that has the line,
, as its perpendicular bisector will have the standard form:
To find the value of C for the specified line segment, substitute the point
And then solve for C:
The equation of the bisected line segment is:
We shall use equations [1] and [2] to find the x coordinate of the point of intersection,
Multiply equation [1] by 3 and equation [2] by 2:
Add equation [3] to equation [4]:
The change in x (
The x coordinate of the other end,
where
To find the corresponding y coordinate,
To other end is at the point
Here is a graph with the two lines and the start and end points plotted: