[FONT="Arial"]Find the equation of the bisector of the acute angle whose equation is
and
Attempt
L1=
L2=
Since, the bisect line is in the middle of the lines then we use the formula
=
Is my answer correct?
Thank you.
Hello, mj.alawami!
Your game plan is correct,
but you have some incorrect minus-signs.
Find the equation of the bisector of the acute angle whose equation is:
. . and
Attempt
. ??
There is no minus-sign in the denominator.
Since, the bisect line is in the middle of the lines,
then we use the formula: . ??
The distances are of opposite signs?
=
Is my answer correct? . . . . Sorry, no
But you were close . . .
Try it again without those extra minus-signs.
Here is a general method which I have been using.
Let the two lines be
Remember to write the two equations in such a way that and .
The eqution of the bisectors are
If ,then use of sign in above equation will give OBTUSE angle bisector
i.e.
is eqution of OBTUSE angle bisector and
gives equation of ACUTE angle bisector
.................................................. .................................................. ..
If ,then use of sign in above equation will give OBTUSE angle bisector
i.e.
is eqution of OBTUSE angle bisector and
is equation of ACUTE angle bisector
.................................................. .............................................
General rule
(i)
where,
(ii)Find sign of
(iii)The use of this sign always gives the OBTUSE angle bisector and the use of other sign gives ACUTE angle bisector