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How to use Algebra to find parallel and perpendicular lines. Parallel Lines. How do we know when two lines are parallel? Their slopes are the same! The slope is the value m in the equation of a line: y = mx + b. Example: Find the equation of the line that is: parallel to y = 2x + 1. and passes though the point (5,4) The slope of y = 2x + 1 is 2.
- Slope
- −0.5
Parallel lines are those that never intersect and are always the same distance apart. Perpendicular lines are those that always intersect each other at right angles. Perpendicular lines are denoted by the symbol ⊥. The symbol || is used to represent parallel lines.
The distance between two lines means that the parallel lines can be determined from one point to another on the opposite line. It is often referred to as the shortest distance between two parallel lines or the perpendicular distance between two lines.
Likewise, parallel lines become perpendicular when one line is rotated 90°. Parallel Curves. Curves can also be parallel when they keep the same distance apart (called "equidistant"), like railroad tracks. The red curve is parallel to the blue curve in both these cases:
May 7, 2024 · Parallel lines in geometry are lines that never intersect and are always at the same distance from each other. On the other hand, perpendicular lines are lines that intersect each other at a right angle, forming a 90° angle.
Perpendicular Lines. Two lines are perpendicular when they are at right angles to each other. The red line is perpendicular to the blue line: Here also: Learn more at perpendicular lines. Perpendicular to a Plane. A line is perpendicular to a plane when it extends directly away from it, like a pencil standing up on a table.
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We can solve for \(m_{1}\) and obtain \(m_{1}=\frac{−1}{m_{2}}\). In this form, we see that perpendicular lines have slopes that are negative reciprocals, or opposite reciprocals. For example, if given a slope \(m=-\frac{5}{8}\) then the slope of a perpendicular line is the opposite reciprocal: \(m_{\perp}=\frac{8}{5}\)
