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What can be said regarding if a line if its slope is negative a)teta is an acute angle.b)teta is an obtuse angle.c)either the line is x-axis or it is parallel to the x-axis.d)none of these.

Posted by Shahana Shahana 2 years, 6 months ago

CBSE > Class 11 > Mathematics

1 answers

Sia ? 2 years, 6 months ago

Let {tex}\theta{/tex} be the angle of inclination of the given line with the positive direction of the x-axis in anticlockwise sense.
Then, its slope is given by m = tan {tex}\theta{/tex}.
If the slope of the line is negative, then
slope = m = tan {tex}\theta{/tex} < 0
{tex}\Rightarrow{/tex} {tex}\theta{/tex} lies between 90° and 180°
{tex}\Rightarrow{/tex} {tex}\theta{/tex} is an obtuse angle.
Therefore, a line of negative slope makes an obtuse angle with the positive direction of x-axis in anticlockwise direction.

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CBSE > Class 11 > Mathematics