Finding Perpendicular, Parallel, Horizontal, and Vertical Lines

Question

You have 2 lines. The first goes through points (7,0) and (4,6) whereas the second goes through points (1,1) and (5,3).

1. Perpendicular
2. Parallel 
3. Horizontal and Vertical 
4. None of the Above

 

You have 2 lines. The first goes through points (6,2) and (4,6) whereas the second goes through points (5,-1) and (1,1).

1. Perpendicular
2. Parallel 
3. Horizontal and Vertical 
4. None of the Above

 

 

Thank you! I'm sure one of you guys can help. You've done brilliant works in the past! I'm working on a study guide and it's hard to fill these in and study when I'm not fully sure what the answers would be. (: 

Answer 1

Determine the slope of the line through each set of coordinates:

m=(y2-y1)/(x2-x1)

 

(7,0) and (4,6):  m = (0-6)/(7-4) = -6/3 = -2

(1,1) and (5,3):  m = (1-3)/(1-5) = -2/-4 = 1/2

Since the slopes are "negative reciprolcals" of each other , the lines are perpendicular.

 

 

 

(6,2) and (4,6): m = (2-6)/(6-4) = -4/2 = -2

(5,-1) and (1,1): m = (-1-1)/(5-1) = -2/4 = -1/2

Since the slopes are neither the same nor negative reciprolcals, this would be None of the above.