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
Douglas K.
Oct 22, 2016

The other end is the point (-168/25, -223/25)

Explanation:

Write the equation of the bisector is slope-intercept form:

y = -3/4x + 1color(white)_[1]

The slope of the bisected line is the negative reciprocal, 4/3. Use the point-slope form of the equation of a line to force the line through point (8,9)

y - 9 = 4/3(x - 8)

y - 9 = 4/3x - 32/3

y = 4/3x - 32/3 + 9

y = 4/3x - 5/3color(white)_[2]

Subtract equation [1] from equation [2]:

0 = (4/3 + 3/4)x - 8/3

Solve for x:

8/3 = 25/12x

This is the x coordinate of the point of intersection:

x = 32/25

The change in x from the given point to the point of intersection:

Deltax = 32/25 - 8 = -168/25

The x coordinate of the other end of the line twice the above added to 8:

x = 8 + 2(-168/25)

x = -136/25

Substitute x = -136/25 into equation [2]:

y = 4/3(-136/25) - 5/3

y = -544/75 - 125/75

y = -669/75 = -223/25

The other end is the point (-168/25, -223/25)

Related questions
See all questions in Perpendicular Bisectors
Impact of this question
1428 views around the world
You can reuse this answer
Creative Commons License