1. Determine if two lines are perpendicular `5x+2y-11=0` and `2x-5y+11=0`
Solution:
When two lines are perpendicular, their slopes are opposite reciprocals of one another or the product of their slopes is -1.
1. Slope of line `5x+2y-11=0`
`5x+2y-11=0`
`:. 2y=-5x+11`
`:. y=-(5x)/(2)+11/2`
`:.` Slope `m_1=-5/2`
2. Slope of line `2x-5y+11=0`
`2x-5y+11=0`
`:. 5y=2x+11`
`:. y=(2x)/(5)+11/5`
`:.` Slope `m_2=2/5`
Now, `m_1*m_2=-5/2 xx 2/5=-1`
Here product is -1, so these two lines are perpendicular
2. Determine if two lines are perpendicular `3x-2y+15=0` and `2x+3y-4=0`
Solution:
When two lines are perpendicular, their slopes are opposite reciprocals of one another or the product of their slopes is -1.
1. Slope of line `3x-2y+15=0`
`3x-2y+15=0`
`:. 2y=3x+15`
`:. y=(3x)/(2)+15/2`
`:.` Slope `m_1=3/2`
2. Slope of line `2x+3y-4=0`
`2x+3y-4=0`
`:. 3y=-2x+4`
`:. y=-(2x)/(3)+4/3`
`:.` Slope `m_2=-2/3`
Now, `m_1*m_2=3/2 xx -2/3=-1`
Here product is -1, so these two lines are perpendicular
3. Determine if two lines are perpendicular `x-y=1` and `2x-3y+1=0`
Solution:
When two lines are perpendicular, their slopes are opposite reciprocals of one another or the product of their slopes is -1.
1. Slope of line `x-y=1`
`x-y=1`
`:. y=x-1`
`:.` Slope `m_1=1`
2. Slope of line `2x-3y+1=0`
`2x-3y+1=0`
`:. 3y=2x+1`
`:. y=(2x)/(3)+1/3`
`:.` Slope `m_2=2/3`
Now, `m_1*m_2=1 xx 2/3=2/3!=-1`
Here product is not -1, so these two lines are not perpendicular
4. Determine if two lines are perpendicular `x-2y+15=0` and `3x+y-4=0`
Solution:
When two lines are perpendicular, their slopes are opposite reciprocals of one another or the product of their slopes is -1.
1. Slope of line `x-2y+15=0`
`x-2y+15=0`
`:. 2y=x+15`
`:. y=(x)/(2)+15/2`
`:.` Slope `m_1=1/2`
2. Slope of line `3x+y-4=0`
`3x+y-4=0`
`:. y=-3x+4`
`:.` Slope `m_2=-3`
Now, `m_1*m_2=1/2 xx -3=-3/2!=-1`
Here product is not -1, so these two lines are not perpendicular
This material is intended as a summary. Use your textbook for detail explanation.
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