Find the angle which a line perpendicular to the line x-y+1=0 makes with the positive direction of x axis - Maths - Straight Lines

Question

Find the angle which a line perpendicular to the line x-y+1=0 makes
with the positive direction of x axis

Vijay Kumar Gupta · Accepted Answer

The equation of line is,  x-y+1=0Write this in slope intercept form  x-y+1=0           -y=-x-1               y=x+1Compare with y-mx+c, we haveThe slope of the line   x-y+1=0 is m=1Let the slope of line perpendicular to x-y+1=0 be m'Then it implies that,    m m'=-1        m'=-1   (since m=1)Let θ be the angle whcih this perpendicular line makes with the positive direction of x-axis, then    tanθ=m'    tanθ=-1    tanθ=-tanπ4    tanθ=tanπ-π4    tanθ=tan3π4          θ=3π4