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?
Practice Questions
1 question
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?
m1 + m2 = 0
m1 * m2 = 1
m1 - m2 = 0
m1 * m2 = -1
For two lines to be perpendicular, the product of their slopes must equal -1.
Questions & Step-by-step Solutions
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Q
Q: 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?
Solution: For two lines to be perpendicular, the product of their slopes must equal -1.
Steps: 4
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.
