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1. The lines 6x - ny + 5 = 0 and x + 2y + 4 = 0 are perpendicular.

What is the value of n?

 

2. What is the area of the triangle bounded by the line x + 2y = 10, a line with an infinite number of x-intercepts, and a line with an infinite number of y-intercepts?

 Jun 9, 2020
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1)  The line  x + 2y + 4  =  0   --->   2y  =  -x - 4   --->   y  =  -½x - 2   --->   m  =  -½.

 

      Since the line  6x - ny + 5  =  0  is perpendicular to the other line, its slope must be  +2.

 

      6x - ny + 5  =  0   --->   -ny  =  -6x - 5   --->   ny  =  6x + 5   --->   n  =  (6/n)x + 5/n

      The slope of this line is  6/n.

      This slope must equal +2   --->   6/n  =  2   --->   6  =  2n   --->   n  =  3

 

2)  x + 2y  =  10  has these intercepts  (0,5)  and  (10,0).

 

     The line with an infinite number of x-intercepts is the x-axis.

     The line with an infinite number of y-intercepts is the y-axis.

     

      The vertices of the triangle are  (0,0),  (0,5),  and  (10,0).

      The area  =  ½·5·10  =  25.

 Jun 9, 2020

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