Pregunta
Are these two lines parallel, perpendicular or neither?
Ask by Franklin Gray. in Dominican Republic
Jan 08,2025
Solución de tutoría real
Respuesta verificada por el tutor
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To determine if two lines are parallel, perpendicular, or neither, compare their slopes. If the slopes are equal, the lines are parallel. If the product of the slopes is \(-1\), they are perpendicular. If neither condition is met, the lines are neither parallel nor perpendicular. Please provide the lines' equations for analysis.
Solución
To determine whether two lines are parallel, perpendicular, or neither, we need to know their equations. The general form of a line's equation is \(y = mx + b\), where \(m\) is the slope.
1. **Parallel Lines**: Two lines are parallel if they have the same slope (\(m_1 = m_2\)).
2. **Perpendicular Lines**: Two lines are perpendicular if the product of their slopes is \(-1\) (\(m_1 \cdot m_2 = -1\)).
3. **Neither**: If neither condition is met, the lines are neither parallel nor perpendicular.
Please provide the equations of the two lines so I can analyze them for you.
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Simplifique esta solución Mind Expander
To determine if two lines are parallel, perpendicular, or neither, you can analyze their slopes. If the slopes are equal, the lines are parallel. If the product of their slopes equals -1, they are perpendicular. For example, if you have one line with a slope of 2 and another with a slope of -1/2, these lines are perpendicular because 2 * (-1/2) = -1! Now, if you're working with a coordinate system, remember that vertical lines have an undefined slope, while horizontal lines have a slope of 0. An easy rule of thumb is: horizontal and vertical lines are always perpendicular! So, keep an eye out for those angles!
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