are the lines through each points parallel or perpendicular. (2,4) (-1,-1) (8,0) (11,5) solve
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are the lines through each pair of points parallel or perpendicular to each other ?
To determine if the lines through each pair of points are parallel or perpendicular, we need to calculate the slopes of the line segments formed by these points.
The formula to calculate the slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slopes:
For the first pair of points (2, 4) and (-1, -1):
m1 = (-1 - 4) / (-1 - 2) = -5 / -3 = 5/3
For the second pair of points (-1, -1) and (8, 0):
m2 = (0 - (-1)) / (8 - (-1)) = 1 / 9
For the third pair of points (8, 0) and (11, 5):
m3 = (5 - 0) / (11 - 8) = 5/3
Since the slope of the line through the first pair of points (5/3) is equal to the slope of the line through the third pair of points (5/3), we can conclude that these lines are parallel.
The slope of the line through the second pair of points (1/9) is not equal to the slopes of the lines through the first and third pairs, so it is not parallel to them. However, to determine if it is perpendicular to the other lines, we need to calculate the negative reciprocal of the slope.
To find the negative reciprocal of a number, we take its reciprocal (1/x) and multiply it by -1.
The negative reciprocal of 1/9 is -9.
Since the negative reciprocal of the slope between the second pair of points (-9) is equal to the slopes of the lines through the first and third pairs (5/3), we can conclude that the lines through these points are perpendicular to each other.
Therefore, we have one set of parallel lines (the lines through the first and third pairs of points) and one set of perpendicular lines (the lines through the second pair of points).