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?
+23246 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.
