Which is the correct answer?

Question

Determine whether the lines through the given pairs of points are parallel. A (2, - 3), B (- 2, - 11) and C (1, 2), D (- 1, 6)

 

A.
The lines through the given pairs of points are not parallel.

B.
The lines through the given pairs of points are parallel.
 

Answer 1

ANSWER: The answer is choice A, the lines through the given pairs of points are not parallel

 

If two lines are parallel, then they must have the same slope. Therefore, two determine the answer to this problem, you must determine the slopes of the lines. If the slopes are the same, the lines are parallel. If the slopes are different, the lines are not parallel.

 

Slope is the rise over the run or the difference in the y values divided by the difference in the x values

 

Start with the first pair of points. Subtract the x values and divide this by the difference of the y values

 

(-11--3)/(-2-2)

(-11+3)/(-2+-2); remember that when you subtract it is the same as adding the opposite

-8/-4

2

So the slope of the first line is 2

 

Now do the same thing with the second pair of points

 

(6-2)/(-1-1)

4/-2

-2

So the slope of the second line is -2

 

The slopes of the first line is 2 and the slope of the second line is -2. Since the slopes are not the same, the lines are not parallel.