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)
Thank you :D
To determine if two lines are parallel, perpendicular, or neither, we need to find the slopes of the lines.
The formula to find the slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
For Line 1:
Coordinates: (-6, 10), (4, -2)
Using the slope formula:
m1 = (-2 - 10) / (4 - -6)
= -12 / 10
= -6 / 5
For Line 2:
Coordinates: (-8, -6), (0, 4)
Using the slope formula:
m2 = (4 - -6) / (0 - -8)
= 10 / 8
= 5 / 4
If the two slopes are equal, then the lines are parallel. If the slopes are negative reciprocals of each other, then the lines are perpendicular. Otherwise, the lines are neither parallel nor perpendicular.
Comparing the slopes:
m1 = -6 / 5
m2 = 5 / 4
The slopes are neither equal nor negative reciprocals of each other. Therefore, the lines through the given points are neither parallel nor perpendicular.
To determine whether two lines are parallel, perpendicular, or neither, we can use the slopes of the lines.
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)
For Line 1:
Point 1: (x1, y1) = (-6, 10)
Point 2: (x2, y2) = (4, -2)
slope1 = (-2 - 10) / (4 - (-6))
= (-2 - 10) / (4 + 6)
= -12 / 10
= -1.2
For Line 2:
Point 1: (x1, y1) = (-8, -6)
Point 2: (x2, y2) = (0, 4)
slope2 = (4 - (-6)) / (0 - (-8))
= (4 + 6) / (0 + 8)
= 10 / 8
= 1.25
Since the slopes of Line 1 (-1.2) and Line 2 (1.25) are not equal, the lines are not parallel.
To determine if the lines are perpendicular, we check if the product of the slopes is -1.
slope1 * slope2 = (-1.2) * (1.25)
= -1.5
The product of the slopes is not equal to -1, so the lines are not perpendicular either.
Therefore, the lines passing through the given points, Line 1 and Line 2, are neither parallel nor perpendicular to each other.
The answer would be "parallel, perpendicular or neither"
A numerical answer would not make any sense
find the slope of line1 and line2
If they are equal, the lines are perpendicular
if the slopes are opposite and reciprocals of each other, the lines are perpendicular.
If anything else, then neither.