(-3,8) (-3,-2) does the line through the first set of points intersect with the line through the second set of points
To determine if the line through the first set of points (-3,8) and (-3,-2) intersects with the line through the second set of points, we need to find the equations of both lines and see if they have a point of intersection.
The equation of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Given the first set of points (-3,8) and (-3,-2), we can determine the equation of the line passing through them.
Slope (m) = (change in y)/(change in x) = (-2 - 8)/(-3 - (-3)) = (-10)/(0) = undefined.
Since the slope is undefined, the line is vertical, and its equation can be written as x = -3.
For the second set of points (-3,8) and (-3,-2), we get the same vertical line equation: x = -3.
Since both lines have the same equation x = -3, they are coincident or overlapping. Therefore, they intersect at every point on the line x = -3.
To determine if the line through the first set of points intersects with the line through the second set of points, we need to find the equations of both lines and then see if they intersect at any point.
Let's start by finding the equation of the line through the first set of points (-3, 8) and (-3, -2). Since both points have the same x-coordinate, we know that the line is vertical and parallel to the y-axis. The equation of a vertical line is x = a, where 'a' is the x-coordinate of any point on the line.
In this case, since the x-coordinate of both points is -3, the equation of the line through the first set of points is x = -3.
Now, let's find the equation of the line through the second set of points (-3, 8) and (-3, -2). Again, since both points have the same x-coordinate, we know that the line is vertical and parallel to the y-axis. Therefore, the equation of the line through the second set of points is also x = -3.
Since both lines are vertical and parallel to each other, they don't intersect at any point. Therefore, the line through the first set of points does not intersect with the line through the second set of points.
To determine if the line through the first set of points intersects with the line through the second set of points, we need to find the slopes of the two lines and check if they are equal.
The slope of a line can be found using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
So, for the first set of points (-3, 8) and (-3, -2), the slope of the line through these points is:
slope₁ = (-2 - 8) / (-3 - -3) = -10 / 0
The formula gives us an undefined value for the slope because the denominator is zero. This means that the line through the first set of points is a vertical line.
Next, for the second set of points (-3, -2) and (-3, 8), the slope of the line through these points is:
slope₂ = (8 - (-2)) / (-3 - (-3)) = 10 / 0
Similar to the first set of points, the slope is undefined for the second set as well because the denominator is zero. This means that the line through the second set of points is also a vertical line.
Since both lines are vertical and their slopes are undefined, they do not intersect.