A line contains the points (0, -2) and (1,3). Another line graphed in the same coordinate plane contains the points (3, -1) and (-2,0).
Based on the slope of these lines, are they parallel, perpendicular or neither?
(0,-2),(1,3).
(3,-1),(-2,0).
m1 = (3-(-2)) / (1-0) = 5/1 = 5.
m2 = (0-(-1)) / (-2-3) = 1/-5 = -1/5.
mi and m2 are negative reciprocals of each other.Therefore, the lines are
perpendicular.
To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The slope of a line can be calculated using the formula:
slope = (change in y) / (change in x)
Let's calculate the slopes for both lines:
For the first line:
Change in y = 3 - (-2) = 5
Change in x = 1 - 0 = 1
Therefore, the slope of the first line is 5/1 = 5.
For the second line:
Change in y = 0 - (-1) = 1
Change in x = -2 - 3 = -5
Therefore, the slope of the second line is 1 / -5 = -1/5.
Now, let's compare the slopes:
If the slopes are equal, the lines are parallel.
If the slopes are negative reciprocals of each other, the lines are perpendicular.
If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
Comparing the slopes of the two lines, we have:
5 and -1/5
Since the slopes are not equal and not negative reciprocals, the two lines are neither parallel nor perpendicular to each other.