What is the value of x so that the line segment with endpoints W(x, -2) and X(5, -4) is parallel to the line segment with endpoints Y(2, 2) and Z(5, 6)?

Question

What is the value of x so that the line segment with endpoints W(x, −2) and X(5, −4) is parallel to the line segment with endpoints Y(2, 2) and Z(5, 6)?

Answer 1

You need to find the slope of the line segment that you know both endpoints of.  Since you know the line segments are parallel, the two line segments need to have the same slope.

 

Slope = y2-y1/x2-x1

 

Slope of Line Segment YZ = 6-2/5-2 = 4/3

 

Now you have to find the point that will make the second line segment have the same slope.

 

Slope of Line Segment WX=

-4 - (-2) = -2

   5 - x      5-x

 

In order to find the common denominator of the second slope, you have to set it equal to the first slope, and find an equivalent fraction.

 

4 = -2    3 x (-2) = 4y   -> -6 = 4y  y = -1.5

3     y

 

Now that you know the denominator of the slope for Line Segment WX is -1.5, you can solve for x 

 

5-x = -1.5

 

Answer 2

Parallel lines have the same slope.  Find the slope between points Y and Z.  Then use that slope to write an equation using points W and X.

 

Slope between Y and Z:

 

slope = (6 - 2) / (5 - 2)

 

        = 4 / 3

 

 

Slope between W and X:

 

(-4 - (-2)) / (5 - x) = 4 / 3

 

-2 / (5 - x) = 4 / 3

 

4(5 - x) = -6

 

20 - 4x = -6

 

 

Continue from here to solve for x.