Respuesta :
The equation of the bisector of angle OAB is y=x
If E is the point of intersection of this bisector and line through A and B then the co-ordinates of E is (40/3,40/3)
Since E is the point of intersection of the bisector of angle OAB and line A and B hence we can say OA:OB=AE:EB
Since point O is the origin hence we can say the co-ordinates of point O are (0,0) and the angle bisector of the angle OAB makes and angle of 45 degree from x axis, So by the formula of Line passing through origin (y= mx )
where ,
∅=angle made by the bisector the angle OAB to the x axis(i.e. 45 degree)
m=tan∅
now using substitution method ,
m=tan45
m=1
the equation of the bisector of angle OAB is y=x
Now, the equation of the line passing through point A(5,0) and point B(0,8) by formula,
(y-y1)={(y2-y1)/(x2-x1)}*(x-x1)
here , y1=0, x1=5, y2=8, x2=0
again by substitution method,
(y-0)={(8-0)/(0-5)}*(x-5)
y={8/-5}*(x-5)
8x - 5y = 40
point E is the intersection of 8x - 5y = 40 and y=x the solving these two equations by substitution method we get;
x=40/3
y=40/3
the co-ordinates of point E are (40/3,40/3)
E is the intersection point of the bisector of the angle OAB and the line through point A and B ,
on comparing triangle OEA and triangle OEB we can say that,
OA:OB= AE:EB
Read more about substitution method here:
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