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Determine whether the lines passing

through the pairs of points are parallel,
perpendicular or neither.
• Line a: (6, 2) and (9, 3)
• Line b: (1, 11) and (3,5)

1 Answer

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Answer:

Lines a and b are perpendicular

Explanation:

  • In order to determine whether the lines passing through the pairs of points are parallel, perpendicular, or neither, we'll first need to know the slopes of the two lines.
  • We can find the slope (m) of a line given two points on the line using the slope formula, which is given by:

m = (y2 - y1) / (x2 - x1), where

  • (x1, y1) is one point on the line,
  • and (x2, y2) is another point on the line.

Slope of line a:

To find the slope of line a, we can plug in (6, 2) for (x1, y1) and (9, 3) for (x2, y2):

m = (3 - 2) / (9 - 6)

m = 1/3

Thus, the slope of line a is 1/3.

Slope of line b:

To find the slope of line b, we can plug in (1, 11) for (x1, y1) and (3, 5) for (x2, y2):

m = (5 - 11) / (3 - 1)

m = -6 / 2

m = -3

Thus, the slope of line b is -3.

Determining whether the lines are perpendicular:

The slopes of perpendicular lines are negative reciprocals of each other, as show by the following formula:

m2 = -1 / m1, where

  • m2 is the slope of one line,
  • and m1 is the slope of the other line.

If we allow 1/3 to be m1, we see that -1 / (1/3) = -1 * 3 = -3

Thus, lines a and b are perpendicular.

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