two lines l and m are perpendicular to lines n and p respectively.If n and p intersect then prove that l and m also intersect
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Let the slope of I = a
the slope of m = b
When two lines are perpendicular, their slopes are opposite reciprocals of each other, and the product of the slopes = -1
Since line I and m intersect a ≠ -1/b
Slope of n = 1/a
Slope of p = -1/b
Slope of n is not the opposite reciprocal of the slope of p
Product of the slopes:
-1/a x -1/b = 1/ab
1/ab ≠ -1
These means that line n and line p are not parallel hence, the lines also intersect
the slope of m = b
When two lines are perpendicular, their slopes are opposite reciprocals of each other, and the product of the slopes = -1
Since line I and m intersect a ≠ -1/b
Slope of n = 1/a
Slope of p = -1/b
Slope of n is not the opposite reciprocal of the slope of p
Product of the slopes:
-1/a x -1/b = 1/ab
1/ab ≠ -1
These means that line n and line p are not parallel hence, the lines also intersect
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