True or false:
Perpendicular lines have slopes that are reciprocals of one another.
false
NEGATIVE reciprocals
True.
To determine if this statement is true or false, we need to understand the concept of perpendicular lines and how their slopes relate to each other.
Two lines are perpendicular if they intersect at a right angle, forming a 90-degree angle between them. The slope of a line represents how steeply it inclines or declines as it moves along the x-axis.
If two lines are perpendicular, their slopes are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of the other line is -1/m.
To calculate the slope of a line, you need two points on the line. Let's assume the coordinates of the two points are (x1, y1) and (x2, y2).
The slope (m) can be determined using the formula:
m = (y2 - y1) / (x2 - x1)
If two lines are perpendicular, their slopes satisfy the equation: m₁ * m₂ = -1, where m₁ is the slope of the first line and m₂ is the slope of the second line.
Therefore, the statement is true: perpendicular lines have slopes that are reciprocals of one another.