Negative Reciprocal

Definition

The negative reciprocal of a number is the negative value of the reciprocal of that number. The reciprocal of a number is the value obtained by dividing 1 by that number, and the negative reciprocal is the negative version of this value.

5 Must Know Facts For Your Next Test

1. The negative reciprocal of a number is the opposite of the reciprocal of that number, obtained by multiplying the reciprocal by -1.
2. The negative reciprocal of a number is often denoted as $-1/x$ or $-\dfrac{1}{x}$.
3. The negative reciprocal of a number is useful in finding the equation of a line that is perpendicular to another line.
4. The slope of a line that is perpendicular to another line is the negative reciprocal of the slope of the original line.
5. The negative reciprocal is an important concept in the context of finding the equation of a line, as it allows for the determination of the slope of a perpendicular line.

Review Questions

• Explain how the negative reciprocal of a number is calculated and how it relates to the reciprocal of a number.
  • The negative reciprocal of a number is calculated by first finding the reciprocal of the number, which is done by dividing 1 by the original number. The negative reciprocal is then obtained by multiplying the reciprocal by -1. For example, if the original number is 4, the reciprocal is 1/4, and the negative reciprocal is -1/4. The negative reciprocal represents the opposite or inverse of the original reciprocal value.
• Describe the relationship between the negative reciprocal of a number and the slope of a line that is perpendicular to another line.
  • The negative reciprocal of a number is closely related to the slope of a line that is perpendicular to another line. Specifically, the slope of a line that is perpendicular to another line is equal to the negative reciprocal of the slope of the original line. This means that if the slope of one line is $m$, the slope of the perpendicular line will be $-1/m$, or the negative reciprocal of $m$. This relationship is important in the context of finding the equation of a line, as the negative reciprocal can be used to determine the slope of a perpendicular line.
• Explain how the negative reciprocal of a number can be used to write the equation of a line in slope-intercept form when the equation of a perpendicular line is given.
  • When the equation of a line in slope-intercept form, $y = mx + b$, is known, the negative reciprocal of the slope $m$ can be used to determine the slope of a line that is perpendicular to the original line. Specifically, the slope of the perpendicular line will be $-1/m$, the negative reciprocal of the original slope. This relationship can then be used to write the equation of the perpendicular line in slope-intercept form, $y = (-1/m)x + b'$, where $b'$ represents the y-intercept of the perpendicular line. By using the negative reciprocal of the original slope, the equation of the perpendicular line can be easily determined.

Related terms

Reciprocal: The reciprocal of a number is the value obtained by dividing 1 by that number, representing the inverse or multiplicative inverse of the original number.

Slope: The slope of a line is a measure of its steepness, representing the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line.

Slope-Intercept Form: The slope-intercept form of a linear equation is $y = mx + b$, where $m$ represents the slope of the line and $b$ represents the y-intercept.