Question

Mathematics

Decide whether the lines given are parallel, perpendicular, or neither.

The line through and .

The line through and .

The line through

The line through

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Best Answer

To determine if the two lines are parallel, perpendicular, or neither, we need to find the slopes of the two lines.

The slope of the first line through and is:

The slope of the first line through

The slope of the second line through and is:

Since the product of the slopes is:

which is not equal to , the two lines are not perpendicular.

Furthermore, the slopes are negative reciprocals of each other, which tells us that the two lines are perpendicular if the sign of one of the slopes is flipped. Since neither slope needs to be flipped, the two lines are not perpendicular either.

Therefore, the two lines are neither parallel nor perpendicular.

Furthermore, the slopes are negative reciprocals of each other, which tells us that the two lines are perpendicular if the sign of one of the slopes is flipped. Since neither slope needs to be flipped, the two lines are not perpendicular either.

Therefore, the two lines are neither parallel nor perpendicular.