Question

A line segment is bisected by a line with the equation `-3 y + x = 1`. If one end of the line segment is at `(1 ,6 )`, where is the other end?

Answer 1

The other end is a `(4.6, -4.8)`

Explanation:

Write the equation for the bisector in slope-intercept form:

`y = 1/3x - 1/3` `[1]`

The slope is, `m = 1/3`

The slope, n, for the bisected line is, `n = -1/m = -1/(1/3) = -3`

Use the slope and the point, `(1, 6)` into the slope, `-3`, into the slope-intercept form of a line and then solve for b:

`6 = -3(1) + b`

`b = 9`

The equation for the bisected line is:

`y = -3x + 9` `[2]`

Subtract equation `[2]` from equation `[1]`

`y - y= 1/3x + 3x - 1/3 - 9`

`0 = 10/3x - 28/3`

The x coordinate of the point of intersection is:

`x = 2.8`

To go from 1 to 2.8, the x coordinate increased 1.8, therefore, to go to the other end of the line x coordinate must increase twice that much, 3.6.

`x = 1 + 3.6 = 4.6`

This is the x coordinate of the other end of the line.

To find the y coordinate, substitute 4.6 for x into equation `[2]`

#y = -3(4.6) + 9

`y = -4.8`