QuestionDetermine if the lines , , and are parallel, perpendicular, or neither.
Studdy Solution
STEP 1
Assumptions1. The equations of the lines are given in the form or .
. Two lines are parallel if their slopes are equal.
3. Two lines are perpendicular if their slopes are negative reciprocals of each other (i.e., ).
4. If neither condition is met, the lines are neither parallel nor perpendicular.
STEP 2
First, we need to rewrite the equations of the lines in the form , where is the slope of the line.
For Line1, we have , which can be rewritten as .
For Line2, we have , which can be rewritten as .
For Line, we have .
STEP 3
Now, we can compare the slopes of each pair of lines to determine whether they are parallel, perpendicular, or neither.
The slope of Line1 is , the slope of Line2 is , and the slope of Line3 is .
STEP 4
Comparing Line1 and Line2, we see that their slopes are not equal and they are not negative reciprocals of each other. Therefore, Line1 and Line2 are neither parallel nor perpendicular.
STEP 5
Comparing Line1 and Line3, we see that their slopes are not equal and they are not negative reciprocals of each other. Therefore, Line1 and Line3 are neither parallel nor perpendicular.
STEP 6
Comparing Line2 and Line3, we see that their slopes are equal. Therefore, Line2 and Line3 are parallel.
In conclusion, Line2 and Line3 are parallel, while the other pairs of lines are neither parallel nor perpendicular.
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