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)
To determine the relationship between the lines through these pairs of points, we can first calculate the slopes of the lines.
The slope of a line passing through the points (x₁, y₁) and (x₂, y₂) is given by:
slope = (y₂ - y₁) / (x₂ - x₁)
Let's calculate the slopes for Line 1 and Line 2:
For Line 1: (-3, 2) and (4, 6)
slope₁ = (6 - 2) / (4 - (-3))
slope₁ = 4 / 7
For Line 2: (-5, 7) and (-9, 14)
slope₂ = (14 - 7) / (-9 - (-5))
slope₂ = 7 / -4
slope₂ = -7/4
Since the slopes of the two lines are different (slope₁ = 4/7 and slope₂ = -7/4), the lines are not parallel.
To determine if the lines are perpendicular, we can check if the product of their slopes is -1.
slope₁ * slope₂ = (4/7) * (-7/4)
slope₁ * slope₂ = -1
Since the product of the slopes is -1, the lines are perpendicular.
Therefore, the lines through the given pairs of points are perpendicular.
To determine whether the lines through these pairs of points are parallel, perpendicular, or neither, we need to 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 = (6 - 2) / (4 - (-3))
= 4 / 7
For Line 2: (-5, 7) and (-9, 14)
slope = (14 - 7) / (-9 - (-5))
= 7 / (-4)
= -7 / 4
If the slopes of two lines are equal, then the lines are parallel. If the product of their slopes is -1, then the lines are perpendicular. Otherwise, they are neither parallel nor perpendicular.
Comparing the slopes, we have:
Slope of Line 1 = 4/7
Slope of Line 2 = -7/4
Since the slopes are neither equal nor the negative reciprocal of each other, the lines through these pairs of points are neither parallel nor perpendicular.
To determine whether two lines are parallel, perpendicular, or neither, we need to examine their slopes.
1. First, let's find the slope of Line 1 using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's assign the coordinates of Line 1 as follows:
Point 1: (-3, 2) -> (x1, y1)
Point 2: (4, 6) -> (x2, y2)
Plugging in the values, we get:
slope of Line 1 = (6 - 2) / (4 - (-3))
= 4 / 7
2. Now, let's find the slope of Line 2 using the same formula:
Let's assign the coordinates of Line 2 as follows:
Point 1: (-5, 7) -> (x1, y1)
Point 2: (-9, 14) -> (x2, y2)
Plugging in the values, we get:
slope of Line 2 = (14 - 7) / (-9 - (-5))
= 7 / -4
= -7/4
3. Since two lines are parallel if and only if their slopes are equal, we can compare the slopes we found:
slope of Line 1 = 4/7
slope of Line 2 = -7/4
Since the slopes are not equal, Line 1 and Line 2 are not parallel.
4. Two lines are perpendicular if and only if the product of their slopes is -1. Let's check if Line 1 and Line 2 are perpendicular:
product of slopes = (4/7) * (-7/4)
= -1
The product of the slopes is -1, which means Line 1 and Line 2 are perpendicular.
In summary, Line 1 and Line 2 are perpendicular to each other.