Tell whether the lines through these pairs of points are parallel, perpendicular, or neither. Line 1: (-3, 2) and (4, 6); Line 2: (-5, 7) and (-9, 14)(1 point) Responses parallel parallel perpendicular perpendicular neither
To determine whether the lines are parallel, perpendicular, or neither, we can find 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)
For Line 1: (-3, 2) and (4, 6)
Slope_1 = (6 - 2) / (4 - (-3))
= 4 / 7
For Line 2: (-5, 7) and (-9, 14)
Slope_2 = (14 - 7) / (-9 - (-5))
= 7 / -4
= -7/4
Since the slopes of Line 1 and Line 2 are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.
Therefore, the answer is neither.
To determine whether two lines are parallel, perpendicular, or neither, we need to find the slope of each line.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the formula:
slope (m) = (y₂ - y₁) / (x₂ - x₁)
For Line 1: (-3, 2) and (4, 6)
slope₁ = (6 - 2) / (4 - (-3))
= 4 / 7
For Line 2: (-5, 7) and (-9, 14)
slope₂ = (14 - 7) / (-9 - (-5))
= 7 / -4
= -7/4
Now, let's compare the slopes of the two lines:
slope₁ = 4 / 7
slope₂ = -7 / 4
Since the slopes are not equal, the lines are neither parallel nor perpendicular.
To determine if two lines are parallel, perpendicular, or neither, we can calculate their slopes.
The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slopes for Line 1 and Line 2:
For Line 1:
(x1, y1) = (-3, 2)
(x2, y2) = (4, 6)
m1 = (6 - 2) / (4 - (-3))
m1 = 4 / 7
For Line 2:
(x1, y1) = (-5, 7)
(x2, y2) = (-9, 14)
m2 = (14 - 7) / (-9 - (-5))
m2 = 7 / -4
Now, let's compare the slopes:
If the slopes are equal, the lines are parallel.
If the slopes are negative reciprocals of each other (i.e., the product of their slopes is -1), the lines are perpendicular.
Otherwise, the lines are neither parallel nor perpendicular.
Let's calculate:
m1 = 4/7 and m2 = 7/-4
Since the product of these slopes is (-1) * (1), which is -1, we can conclude that the lines are perpendicular.
Therefore, Line 1 and Line 2 are perpendicular.