A line segment is bisected by a line with the equation 4 y - 3 x = 2 . If one end of the line segment is at ( 2 , 5 ), where is the other end?

1 Answer
Alan P.
Oct 5, 2016

The other end will be any point on the line 4y-3x=-10

Explanation:

Consider the vertical line x=2 which passes through (2,5)

x=2 will intersect 4y-3x=2 at (2,2)

(2,5) is 3 units vertically above (2,2);
that is (2,5) is vertically 3 units above 4y-3x=2

Any point 3 units vertically below 4y-3x=2 will provide a second point which together with (2,5) form a line segment bisected by 4y-3x=2

Re-writing 4y-3x=2 in slope-intercept form: y=3/4x+2/4

The y-intercept for a line 3 units below 3=3/4x+2/4 will be at 2/4-3=-10/4

Therefore this second line will have a slope-intercept equation of
color(white)("XXX")y=3/4x-10/4
or in a form similar to the initial equation:
color(white)("XXX")4y-3x=-10

The image below may help:enter image source here

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