Question

If A( x, 1), B( -3,7), C( -5, 9), and D( 5, 4), find the value of x so that line AB is parallel to line CD.

Answer 1

The slope of CD = (9-4) / (-5-5) = 5/-10 = -1/2

The slope of AB must also be -1/2

Slope of AB = (1-7) / (x - -3) = -6 / (x+3)

For AB to equal -1/2, the denominator needs to be twice as much as the numerator, so set up an equation:

2(x+3) = 12

Now solve for x:

2x +6 = 12

2x = 18

x = 18/2

x = 9