Show that for all values of m the straight line x(2m-3)+y(3-m)+1-2m=0 pass thru the point of intersection of two fixed lines.for what values of m does the given line bisect the angles between the two fixed lines?

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Answer 1 · 2016-05-22T19:17:36

#m = 2# and #m = 0#

Solving the system of equations

#x (2 m - 3) + y (3 - m) + 1 - 2 m=0#
#x (2 n - 3) + y (3 - n) + 1 - 2 n = 0#

for #x,y# we get

#x = 5/3, y=4/3#

The bisection is obtained making (straight declivity)

#(2m-3)/(3-m) = 1-> m = 2# and
#(2m-3)/(3-m) = -1-> m = 0#