let the slope of the line be m.
The slopes of the given lines are 12/5 and 3/4. As they are equally inclined to the two unknown lines, we have
(m+12/5)/(1-12m/5) = -( m+3/4)/1-3m/4)
Solving for m we get m = 7/9 and m=-9/7
(Please notify me if my m values are wrong)
So putting these values in point slope formula, the equations are:
y-5 = 7/9(x-4)
and y-5=-9/7(x-4) are the two lines.
first draw the diagram
solve the given equations then u get one co ordinate of the side as u have orthocenter u get the slope of the line
as required equation of the line and above line is perpendicular so product of slopes is -1. then v get the slope of required line
nw we require one coordinate
let triangle be ABC , O orthocenter , D, E , F the points wer othocenter meets BC , CA , AB
let equation of AB be 3x-2y+6=0 n equation of AC be 4x+7y+5=0
OB is perp to AC we no slope of AC so we get of OB too
as OB passes throgh O we get the equation of OB
solvin OB n AB we get one coordinate of side then we have slope n coordinate we can find equation
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