A line segment is bisected by a line with the equation # 4 y + 3 x = 4 #. If one end of the line segment is at #( 8 , 9 )#, where is the other end?
1 Answer
The other end is the point
Explanation:
Write the equation of the bisector is slope-intercept form:
The slope of the bisected line is the negative reciprocal,
Subtract equation [1] from equation [2]:
Solve for x:
This is the x coordinate of the point of intersection:
The change in x from the given point to the point of intersection:
The x coordinate of the other end of the line twice the above added to 8:
Substitute
The other end is the point