# A line segment is bisected by a line with the equation # 3 y - 7 x = 2 #. If one end of the line segment is at #(7 ,8 )#, where is the other end?

##### 1 Answer

The other end is at the point:

#### Explanation:

Rewrite the given line in slope-intercept form so that we can obtain the slope, m, of the line.

We observe that

The slope, n, of the bisected line is the negative reciprocal of m:

Use this slope and the given point to solve for

The equation of the bisected line is:

Subtract equation [2] from equation [1]:

The x coordinate of the point two lines intersect is:

The change in x from the point

To go to the other end of the line we must move twice that far in same direction:

The add 7 to find the x coordinate of the other end of the line segment:

To find the y coordinate of the other end of the line segment substitute 14/28 for x in equation [2]: