Line Segments

Question

One line segment that the upper point is P(3,10)

 and the bottom point Q(6,1)

 

Then another line that the upper point is R(x,8) and the bottom point is S(5,5) 

 

Find the value of x.

Answer 1

Then Asma, the slopes of the two segments are equal:

 

The slope of the first segment is:

 

slope₁ = (y₂ - y₁)/(x₂ - x₁) = (10 - 1)/(3 - 6) = 9/-3 = -3

 

Since the two slopes are equal we can use this slope to calculate x for the other segment:

 

-3 = (5 - 8)/(5 - x) 

 

Multiply both sides by (5 - x)

 

-3(5 - x) = -3

 

Divide both sides by -3:

 

5 - x = 1

 

Rewrite:

 

x = 5 - 1 = 4

 

Questions?