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The equation of the pair of lines through the origin is given by y = mx. If m1 a

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Question: The equation of the pair of lines through the origin is given by y = mx. If m1 and m2 are the slopes, what is the condition for them to be perpendicular?

Options:

  1. m1 + m2 = 0
  2. m1 * m2 = 1
  3. m1 - m2 = 0
  4. m1 * m2 = -1

Correct Answer: m1 * m2 = -1

Solution: 

For two lines to be perpendicular, the product of their slopes must equal -1.

The equation of the pair of lines through the origin is given by y = mx. If m1 a

Practice Questions

Q1
The equation of the pair of lines through the origin is given by y = mx. If m1 and m2 are the slopes, what is the condition for them to be perpendicular?
  1. m1 + m2 = 0
  2. m1 * m2 = 1
  3. m1 - m2 = 0
  4. m1 * m2 = -1

Questions & Step-by-Step Solutions

The equation of the pair of lines through the origin is given by y = mx. If m1 and m2 are the slopes, what is the condition for them to be perpendicular?
  • Step 1: Understand that the equation of a line through the origin is y = mx, where m is the slope.
  • Step 2: Identify the slopes of the two lines as m1 and m2.
  • Step 3: Recall the condition for two lines to be perpendicular: their slopes must satisfy the equation m1 * m2 = -1.
  • Step 4: This means that if you multiply the slopes of the two lines, the result should be -1 for the lines to be perpendicular.
  • Perpendicular Lines – Two lines are perpendicular if the product of their slopes is -1.
  • Slope of Lines – The slope of a line in the form y = mx is represented by m.
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