# A line segment is bisected by a line with the equation # 2 y + 9 x = 3 #. If one end of the line segment is at #(3 ,2 )#, where is the other end?

##### 1 Answer

The point

#### Explanation:

For a line with a slope that is perpendicular to the given line

Swap the coefficients of x and y, change the sign of one of the coefficients, and set it equal to an arbitrary constant:

To find the value of the constant, substitute the point

The equation of the bisected line is:

Multiply equation [1] by 9 and equation [2] by 2:

Add equation [3] to equation [4]:

This is the x coordinate of intersection.

Let

Let

To find the corresponding y coordinate, substitute the value of