What is a negative reciprocal?

In mathematics, the negative reciprocal of a number is the value obtained by taking the reciprocal of the number and then changing its sign to the opposite. For example, the negative reciprocal of 2 is -1/2, and the negative reciprocal of -3 is 1/3.

The negative reciprocal of a number is important in geometry, particularly in the study of lines and slopes. When two lines are perpendicular to each other, their slopes are negative reciprocals of each other. This is because the product of the slopes of two perpendicular lines is always -1.

In general, the negative reciprocal is used in various mathematical calculations and applications, especially in algebra, trigonometry, and geometry. It plays an important role in understanding the relationships between numbers and shapes, and is a fundamental concept in mathematics.