Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (-6,10), (4,-2)
Line 2: (-8,-6), (0,4)
check the slopes. If equal, the lines are parallel
If they multiply to -1, the lines are perpendicular.
Tell whether the lines containing the following points are parallel, perpendicular or neither:
Line A with points (5, 3) and (-10, 0) and Line B with points (0, -4) and (-2, 6).
To determine whether the lines are parallel, perpendicular, or neither, we can compare their slopes.
The slope of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
For Line 1:
Point 1: (-6, 10)
Point 2: (4, -2)
m1 = (-2 - 10) / (4 - (-6))
= (-12) / (4 + 6)
= (-12) / (10)
= -1.2
For Line 2:
Point 1: (-8, -6)
Point 2: (0, 4)
m2 = (4 - (-6)) / (0 - (-8))
= (4 + 6) / (8)
= 10 / 8
= 1.25
Since the slopes of Line 1 and Line 2 are not equal, the lines are not parallel.
To determine if the lines are perpendicular, we can check if the product of their slopes is -1.
m1 * m2 = -1.2 * 1.25
= -1.5
Since the product of the slopes is not -1, the lines are not perpendicular either. Therefore, the lines are neither parallel nor perpendicular.
To determine if the lines through the given points are parallel, perpendicular, or neither, we need to calculate the slopes of the lines.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slopes for Line 1 and Line 2:
For Line 1: (-6,10), (4,-2)
slope1 = (-2 - 10) / (4 - (-6))
= (-12) / 10
= -6 / 5
For Line 2: (-8,-6), (0,4)
slope2 = (4 - (-6)) / (0 - (-8))
= (4 + 6) / 8
= 10 / 8
= 5 / 4
Now we can compare the slopes:
If the slopes of two lines are equal, then the lines are parallel.
If the slopes of two lines are negative reciprocals of each other (i.e., when multiplied together, equal -1), then the lines are perpendicular.
If the slopes are neither equal nor negative reciprocals, then the lines are neither parallel nor perpendicular.
Let's check:
slope1 = -6 / 5
slope2 = 5 / 4
Since the slopes are not equal and not negative reciprocals of each other (i.e., -6/5 * 5/4 = -30/20 = -3/2 ≠ -1), we can conclude that Line 1 and Line 2 are neither parallel nor perpendicular to each other.