Line A goes through the points (-1, 2) and (-7, 20). Line B goes through the points (3, -4) and (5, -10). Are the two lines parallel, perpendicular, or neither?
Let's find the slopes of the two lines.
The slope of Line A is given by the formula:
m1 = (y2 - y1) / (x2 - x1)
m1 = (20 - 2) / (-7 - (-1))
m1 = 18 / (-6)
m1 = -3
The slope of Line B is given by the formula:
m2 = (y2 - y1) / (x2 - x1)
m2 = (-10 - (-4)) / (5 - 3)
m2 = (-10 + 4) / 2
m2 = -6 / 2
m2 = -3
Since the slopes of both lines are the same (-3), the two lines are parallel.
To determine if two lines are parallel, perpendicular, or neither, we need to find the slopes of the lines. The slope of a line can be calculated using the formula:
slope = (change in y) / (change in x)
For line A, we have the points (-1, 2) and (-7, 20). Let's calculate the slope:
Slope of line A = (20 - 2) / (-7 - (-1))
= 18 / (-6)
= -3
For line B, we have the points (3, -4) and (5, -10). Let's calculate the slope:
Slope of line B = (-10 - (-4)) / (5 - 3)
= -6 / 2
= -3
Since the slopes of both lines A and B are -3, we can conclude that the two lines are parallel.
To determine whether two lines are parallel, perpendicular, or neither, we need to examine the relationship between their slopes. The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slopes of lines A and B:
For Line A:
slope_A = (20 - 2) / (-7 - (-1))
= 18 / (-6)
= -3
For Line B:
slope_B = (-10 - (-4)) / (5 - 3)
= (-10 + 4) / 2
= -3
Comparing the slopes of Line A and Line B, we see that they have the same value: -3.
Since the slopes of the two lines are identical, we can conclude that Line A and Line B are parallel.