Question

Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. if line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (assume that all lines lie in one coordinate plane.)

Answer 1

Slope of line l (m1)=5
Slope of line w(m2)=-1/5
Since,m1×m2=-1 , line 'l' and 'w' are perpendicular.
Since line 'k' doesn't intersect line 'l' ,they must be parallel b'coz they are in the same plane as well.
Here, 'l' is perpendicular to 'w' and parallel to 'k'....so w and k must be perpendicular to each other.
It can be proven:
Since l and k are parallel, their slopes are equal.
So, slope of k (m3)=5
Since m3×m2=-1 ,w and k are perpendicular.
Hence, angle between w and k is 90°