A line segment is bisected by a line with the equation # 3 y + 5 x = 2 #. If one end of the line segment is at #( 5 , 8 )#, where is the other end?
1 Answer
The other end is at
Explanation:
This problem is in the perpendicular bisectors so it is safe to assume that the bisected line is perpendicular; that means that its equation is of the form:
To find the value of c, substitute in the point
The equation of the bisected line is:
The given equation is:
Multiply equation [1] by -3 and equation [2] by 5
Add equations [3] and [4]:
Let
The x coordinate of the other end of the line segment is twice that change added to the starting x coordinate:
To find the y coordinate,
The other end is at