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What is the slope of a line that is perpendicular to a line with a slope of [tex]\(-2\)[/tex]?

A. [tex]\(-1\)[/tex]
B. [tex]\(\frac{1}{2}\)[/tex]
C. [tex]\(2\)[/tex]

(Note: The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.)

Sagot :

GinnyAnswer
To determine the slope of a line that is perpendicular to a given line, we use the concept of negative reciprocals. If you have the slope of a line, the slope of the line that is perpendicular to it is the negative reciprocal of that original slope.

Given:
- The slope of the original line is [tex]\( -2 \)[/tex].

To find the perpendicular slope:
1. First, take the given slope [tex]\( -2 \)[/tex].
2. Find the reciprocal of the slope. The reciprocal of [tex]\( -2 \)[/tex] is [tex]\( -\frac{1}{2} \)[/tex].
3. Then, negate the reciprocal. Negating [tex]\( -\frac{1}{2} \)[/tex] gives us [tex]\( \frac{1}{2} \)[/tex].

Therefore, the slope of the line that is perpendicular to the line with a slope of [tex]\( -2 \)[/tex] is [tex]\( \frac{1}{2} \)[/tex].

The answer is [tex]\( \frac{1}{2} \)[/tex].
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