What is the value of x so that the line segment with endpoints A(x, 1) and B(2, −3) is parallel to the line segment with endpoints C(−5, 2) and D(−3, 5)?

Question

 proofs on the coordinate plane 

Answer 1

The slopes have to be the same.

 

slope of CD is (2-5)/(-5 - -3) = ( 2 + -5)/ ( -5 + 3) = -3/(-2) = 3/2

 

The slope of AB must be 3/2

 

 

 3/2 = (-3 - 1)/(2-x)

 

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

 

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

 

3(2-x) = -8

 

6 - 3x = -8

 

-3x = -14

 

x = 14/3

 

 

CHECK:

 

  (1 - -3)/(14/3 - 2) = 4/(14/3 - 6/3) = 4/(8/3) = 4*3/8 = 12/8 = 3/2