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Question Video: Finding the Slope of a Straight Line given the Slope of a Perpendicular Line Mathematics • 11th Grade

If line ๐ด๐ต โŠฅ line ๐ถ๐ท and the slope of line ๐ด๐ต = 2/5, find the slope of line ๐ถ๐ท.

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Video Transcript

If line ๐ด๐ต is perpendicular to line ๐ถ๐ท and the slope of line ๐ด๐ต equals two-fifths, find the slope of line ๐ถ๐ท.

Here, we are told that we have two perpendicular lines ๐ด๐ต and ๐ถ๐ท. Knowing that two lines are perpendicular means that we know something about the relationship between their slopes. If we define line ๐ด๐ต to have a slope of ๐‘š sub one and line ๐ถ๐ท to have a slope of ๐‘š sub two, then we know that ๐‘š sub two is equal to negative one over ๐‘š sub one. Given that the slope ๐‘š sub one of line ๐ด๐ต is two-fifths, then ๐‘š sub two is equal to negative one over two-fifths. This simplifies to negative five over two. Because these two lines are perpendicular, their slopes will be the negative reciprocal of one another. And so the slope of line ๐ถ๐ท is negative five over two.

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