How to Determine the Ratio by which a Line Divide a Line Segment in Coordinate Geometry Video Lecture - Class 10

in this video we're going to find out
the ratio by which a line is going to
divide a line segment joining the two
points linear equation determine the
ratio in which the line segment 3x plus
y minus 9 divides the line segment
joining the points 1 3 2 7 so the
question is you know saying something
like this suppose we have a point here a
hos coordinate is 1 3 and we have
another point suppose B which has cornet
to 7 now let me join this line and now
it is a segment so now this line segment
a B has been actually divided by another
lines say this is our line it's not a
straight this is my line suppose which
is 3x plus y minus 9 equals to 0 now
this line is intersecting it right at
point this let me say point P whose
cornet is let me suppose X bar Y bar so
this X bar Y bar this P point is
intersecting the line a B right into the
two pieces one piece is a P and another
piece is P B so we have the two piece
you know so we need to find out actually
the ratio you know the ratio in which
this a P and P V are right or you can
say how many person we have in AP and
how many person we have in TV we need to
find out that so again you know you can
choose any ratio you can choose
something like if you want to do faster
then again you can use like qué dicha 1
or sometimes we had used as a lambda
ratio 1 whatever you choose lambda K man
over PA BC what he will choose that's
just a constant that you need to find
out it's like a ratio or as you serve
the best process M 1 ratio M 2 right if
you use this this is the main base you
know actually the base in in Section
formula we use this M 1 ratio M so this
is the main base form liner and by this
method you can do a you can solve this
easily what do you use feed easy I will
be doing both key issue one also and M
one ratio M two also this will be a
little bit maybe a little bit lengthy
right this K ratio one will be a little
bit shorter I feel right faster I feel
so I will be doing this by clear issue
one first
and auditing by the m1 a sham - what do
you feel easy doing that we both are the
same actually you know Cadiz you won
it's a kind of modified version of the
section formula right because there is
only one variable key and here it will
be two variables so it may make you a
little bit a hick to your brain
anyways let's go now I suppose that the
point P is dividing this this this a B
line segment in the ratio k1 okay or you
can say the line is cutting it it with
the key issue one so for the x bar and y
bar our section formula is now when K is
the ratio it will be no K times X 2 plus
X 1 divided by K plus 1 and again K
times y 2 plus y 1 divided by K plus 1
all right I think you know this formula
if you're not knowing this formula then
I'm gonna explain it here it is actually
a you know section formula only it is it
is M 1 X 2 plus M 2 X 1 over m 1 plus M
2 and it's 1 2 2 1 1 2 2 1 right
similarly M 1 Y 2 plus plus M 2 y 1
divided by M 1 plus M 2 here you know
actually if we had imagined something
like K as M 1 + 1 as M 2 then we'll have
this kind of formula so if you replace
this M 1 by K and this M 2 by 1 what
happens let's see we all are going to
replace by this K + 1 so this is K and
this is 1 this is K and this is one
we're just going to replace what you'll
get you'll get exactly this C K times X
- K X 2 plus X 1 right let me - here
you'll get value and studied K X 2 you
know K X 2 + 1 times X 1 X 1 and again K
Y - K Y 2 this is K Y 2
why one you know one times y1 and then
it is m1 plus m2 so k plus 1 k plus 1
alright so now let's do father's so X
bar Y bar so X bar Y bar
so now K times x2 now which one will be
x2 y2 and which one will be x1 y1 always
questions comes there then every time is
to say where this K our m1 comes closer
that part will be x1 y1 all right now if
you see here in this case here is m1 and
here is K so the nearest point for this
M 1 or K this part would like this part
the nearest one is you know the nearest
one is a part so this a part will be
always x1 and y1 if this is x1 and y1
this will be treated as x2 and y2 okay
so now k times X 2 so X 2 is my here now
to this 2 is my X 2 so 2 and then X 1 X
1 is here my y1 and then I'll get K plus
1 and now k y2 so K and Y 2 is here
minus 7 so it is 7 plus y 1 so Y 1 is
here my 3 right divided by K plus 1 let
me raise it properly
my X bar and y bar is going to be now 2
k plus 1 divided by k plus 1 and 7 k 7k
+ 3 divided by k plus 1 so I got my X
bar Y bar I got my X bar Y bar and you
know frame this my X bar Y bar this p
point is actually passing through the
line 3x plus y this this p point lies in
this line in this line right so if I'm
going to replace this X as a x bar and y
as a Y bar then it should satisfy it
right this is rule so
so what I'm going to do since X bar and
y bar passes through passes through the
line 3x plus y minus 9 equals to 0
therefore what I can do now I can do 3 X
bar plus y bar minus 9 equals to 0 so
let me put the value of x bar and y bar
right so 3 what is my X bar here I've
got X bar as a 2 k plus 1 over k plus 1
so 2 k plus 1 over k plus 1 and then
plus and now I have Y bar so now Y bar
is equals to in the yellow color 7q plus
3 right 7 k plus 3 divided by k plus 1
and minus this 9 right so equals 0 it is
everybody had k plus 1 k plus 1 so it is
better to multiply by the k plus 1 and
divide by the k plus 1 further easy
calculation all right now let's go
further you will get now 3 times 2 right
let's multiply this 3 times 2 you will
get 6 k plus 3 and then 7 k plus 3 7 k
plus 3 and then minus 9 k minus 9 whole
divided by k plus 1 equals to 0 now this
k plus 1 will melt bet is 0 so you will
get 0 all right so this whole quantity
now see how much we are going to have
now see this is 6 k plus 7 k cyrene k
minus 9 k that is 4 K and this is 3 K
sorry 3 & 3 that is 6 & 6 plus 6 minus 9
you will get minus 3 equals to 0 so what
I can say that for K is equals to 3 and
K will be 3 over 4 and if nothing is
there there is one all right so it means
yes means we got the K ratio 1 equals to
3 ratio 4 Hey
the answer here is one we got the 3d
show for so the question was demanding
asked the ratio right by which ratio
they were asking and we got the ratio
this is this this m1 ratio is actually
how much well it's coming 13 this m1
ratio we got three and we got em 2 ratio
for though I made a little bit wrong
figure it should be here and there all
right well so three ratio for this line
is dividing this whole segment a-b
all right now if you want to do buy the
m1 or m2 no problem right this is this
will be same and here you will get right
if you if you solve it like key will be
replaced by again m1 and here here is
one more one because X 1 value is here
one right so key x 1 it was 1 so this
one will be replaced by 1 so m2 so
you'll get here like directly I'm going
to write if you put the velop in the
place of K K and 1 if you put the m1 m2
you will get something like this m1 to
m1 plus m2 divided by m1 plus m2 and
here you will get again 7 m1 plus 3 m2
divided by m1 plus m2 right now you got
this point all right
and I'll just again in the place of X
bar and y bar you gonna put this this
value and this value all right so what
do you get here three times this to m1
plus m2 divided by m1 plus m2 right and
then plus y we have so why is this seven
m1 + 3 m2 divided by m1 plus m2 minus 9
we have - then we have so - 9 equals to
0 and since everybody had m1 m1 so I'm
m1 + m2 divided by m1 plus m2 I'm doing
just for the easiness of calculation I'm
doing this right from my sir I've given
so 3 times 2
get 6 m 1 and 3 times 2 m 2 you'll get 3
m 2 and again 7 m 1 7 m 1 and again 3 M
1 3 em - sorry and - 9 m 1 - 9 m 1 - 9 m
2 equals to 0 now let's add and
calculate all them 6 m17 m113 m 1 - 9 m
1 you'll get 4 m 1 right now 3 M - 3 M -
6 m 2 - 9 m 2 that is minus 3 M - it
goes to 0 and you'll get what for M 1
equals to 3 M 2 so you'll get M 1 over m
2 as a 3 over 4 that is that is that is
that is what we get yes M 1 raise your M
2 equals to 3 ratio for so anyhow you do
you'll get the same same same same
answer so for those trends you know who
feels like if you are like doing by the
multiple method if your teachers doing
multiple methods and solving the same
questions you may get the confused so
for those strengths am just telling you
every time every time keep inserting
your brain ok whenever you take the
coordinate problem it lets you do the
section formula then for you guys you
know you always use the same one ratio M
2 formula always means you sex and
formula this the section formula you
don't think knavery I need to use this K
ratio on lambda ratio on naver confusion
these things always use this standard
section formula sometime it may be a
little bit lengthy but every time every
time this will walk naked you need to
get confused on this key issue or lambda
ratio on any shortcuts don't put any
heck on your brain okay
the simplest method always use M M 1 X 2
plus M 2 X 1 divided by M 1 plus M 2
right and M 1 Y 2 plus M 2 y 1 over m 1
plus M 2 this method always you use
that's awesome you know never you'll get
confused and you know use always one
method that becomes you know a kind of a
kind of you know good feelings it gives
in my mind because never you need to
think or the other formulas and they
were you need to remind many more
formulas I hear in
you need remind this on one also this
one also 11 it get confused in also
always is only one formula comfortable
like we did at the last so but some
people feels here if I can understand
why should not and yeah if your
understanding if you're smart enough to
do this then please do that that's
that's not the problem but I'm telling
for those who like who don't want to do
more things like and then who don't want
to stress more on maths for those
peoples ok so we'll be doing more a
couple of more problems of this X and
formula and and that will definitely
give you some good idea to solve the
problems I hope you understand this
problem you enjoy the video will meeting
the next video
catch you there bye bye