A line segment is bisected by line with the equation 3 y - 3 x = 4 . If one end of the line segment is at (2 ,4 ), where is the other end?

1 Answer
Douglas K.
Oct 31, 2016

The other end is at (8/3, -2/3)

Explanation:

Write the equation of the perpendicular bisector in slope-intercept form, y = mx + b:

y = x + 4/3 [1]

The slope of the bisector is m = 1.

To find the slope of the bisected line, use the fact that the slopes of perpendicular are negative reciprocals of each other:

n = -1/m

Therefore, the slope of the bisected line is n = -1.

Use the slope-intercept form of the line, y = nx + b, the slope, n = -1, the given point, (2,4), to write an equation that allows use to find the value of b:

4 = -2 + b

b = 6

The equation of the bisected line is:

y = -x + 6 [2]

Because y = y, we can set the right side of equation [1] equal to the right side of equation [2]:

x + 4/3 = -x + 6

2x = 14/3

x = 7/3

This means that the line segment starts at 2, ( which is 6/3), and goes to 7/3 to intersect with its bisector, therefore the other end of the segment must be twice that far , 8/3

To find the corresponding y coordinate, substitute 8/3 for x in equation [2]

y = -8/3 + 6

y = -2/3

Related questions
See all questions in Perpendicular Bisectors
Impact of this question
1962 views around the world
You can reuse this answer
Creative Commons License