Determine whether the line through
(0, 4) and (2, 0) and the line through
(−2, 3) and (−4, 2) are parallel,
perpendicular, or neither.
neither?
slope of the 1st ... (0 - 4) / (2 - 0) = -2
slope of 2nd ... (2 - 3) / (-4 - -2) = 1/2
slopes are negative reciprocals
lines are perpendicular
Why did the line through (0, 4) and (2, 0) and the line through (-2, 3) and (-4, 2) go to couples therapy?
Because they couldn't decide if they were parallel, perpendicular, or neither! It seems like they just couldn't find any common ground. So, to answer your question, yes, they are neither parallel nor perpendicular. It's like they're stuck in their own little world of line confusion.
To determine whether the lines through the points (0, 4) and (2, 0), and through the points (-2, 3) and (-4, 2) are parallel, perpendicular, or neither, we can compare their slopes.
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 the first line, passing through (0, 4) and (2, 0), the slope is:
slope1 = (0 - 4) / (2 - 0)
= -4 / 2
= -2
For the second line, passing through (-2, 3) and (-4, 2), the slope is:
slope2 = (2 - 3) / (-4 + 2)
= -1 / -2
= 1/2
Since the slopes of the two lines, -2 and 1/2, are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.
To determine whether the lines are parallel, perpendicular, or neither, we need to observe their slopes.
A slope is a measure of how steep a line is and can be calculated using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
Let's calculate the slopes of both lines:
For the line passing through (0, 4) and (2, 0):
Slope1 = (0 - 4) / (2 - 0) = -4 / 2 = -2
For the line passing through (−2, 3) and (−4, 2):
Slope2 = (2 - 3) / (-4 - (-2)) = -1 / (-2) = 1/2
Now we 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.
If neither condition is met, the lines are neither parallel nor perpendicular.
In this case:
Slope1 = -2
Slope2 = 1/2
Since the slopes are not equal, and the product of the slopes is not -1, we can conclude that the lines are neither parallel nor perpendicular.
Therefore, the correct answer is neither.