is the line through points P (-1,-2) and Q(1,2) parallel to the line through the points R(3,-1) and S(5,3)
A. yes they both have a slope of 1/2
B. yes they both have a slope of 2
C. no, the slopes are unrelated to each other
D. yes their slopes are opposite reciprocals of each other
To determine if two lines are parallel, we need to compare their slopes.
Let's find the slope of the line passing through points P and Q. The slope of a line passing through two points (-1, -2) and (1, 2) can be found using the slope formula:
m1 = (y2 - y1) / (x2 - x1)
m1 = (2 - (-2)) / (1 - (-1))
m1 = 4 / 2
m1 = 2
Now, let's find the slope of the line passing through points R and S. The slope of a line passing through two points (3, -1) and (5, 3) can be found using the slope formula:
m2 = (y2 - y1) / (x2 - x1)
m2 = (3 - (-1)) / (5 - 3)
m2 = 4 / 2
m2 = 2
Since the slopes of both lines are equal, we can conclude that the lines are parallel.
Therefore, the correct answer is A. Yes, they both have a slope of 1/2.