Finding the Tri-Section Formula - Coordinate Geometry Video Lecture - Class 9

hello friends here is a third type of
problem in Section former of coordinate
geometry question singer find the
coordinates of the points of tri section
of the line segment joining the points a
2 comma negative 2 and B negative 7
comma 4 right so we need to find out the
two such points that will invite this
line joining these points right this
point and this one joining line so let
me draw a rough like I'm over here
suppose this is our line this is point a
and this is point B right it's
coordinate is 2 comma minus 2 right and
here B is negative 7 comma 4 so here are
such two points suppose here 1 and here
is a 1 right suppose this is P and this
is Q point this P and Q point is
dividing this whole line in equal three
sections
it means question is in krycek-- ssin
right so this is equals to this is
equals to this I mean a P is equals to P
Q is equals to QB right so we need to
find out the coordinates of this P point
and Q point let me shake this point is
x1 y1 and this Q point is x2 and y2
right so I need to find out the
coordinates this P and Q so if I want to
use the section formula then I must know
the ratio by which it is cutting this
right so just see ya this part this part
this part there are three equal parts
and we can say since this is two equal
parts and this is one equal parts so
this is one part and this is one and two
equal parts that so it's two equal part
so what can I say now that this P point
is dividing this AV line in the ratio of
one ratio to right one ratio to this P
point is Deveny and if you talk about
this Q points then see in left side
there are two equal parts right so if we
come here right if you come here
there is two equal parts I mean yeah and
here is one equal bar right so this Q
point is dividing this AV line in two
ratio one and
ppand is dividing this whole IV line in
one ratio to right so let me first find
out the value of this this is this P
point I'm in the coordinates of this P
point right so let me find out first
okay so let me refresh the section
former that is X comma Y is equals to M
1 X 2 plus M 2 X 1 whole divided by M 1
plus M 2 again
M 1 y 2 plus M 2 y 1 1 divided by M 1
plus M 2 right this is our section
formula now I'm applying the section
form line this in this problem right so
let me first find out the P that is X 1
y 1 is equals to M 1 X 2 so let me
suppose this is this point is X 2 y 2
and means here in for this formula only
X 2 y 2 and this will walk as x1 y1 so M
1 M 1 is here 1 so 1 times X 2 that is
minus 7 minus 7 plus M 2 m 2 is here 2
times X 1 that is 2 right holy my advice
M 1 plus M 2 that is M 1 is 1 and M 2 is
2 plus 2 right and again M 1 Y 2 so M 1
is here 1 and Y 2 here is 4 plus M 2
again here 2 times y 1 y 1 is here minus
2 and that is negative 2 right Holy Mary
right and 1 plus M 2 that is 1 plus 2 a
n right so again P X Y is equals to 1
times minus 7 it will be minus 7 plus 2
times 2 that is 4 1 divided by 3 right
again 4 times 1 that is 4 and 2 times 2
but negative so it will be negative 4
right
so negative 4 1 upon 2 right 1 plus 2
that will be 3 right so what we guard
here that minus 4 plus 4 so plus minus
it will be minus
always the sign of the greater and the
operation will be negative also means a
- will be so 7 plus 4 will be 3 since it
is negative so negative 3 divided by 3 +
4 - 4 that is 0 divided by 3 right so it
will be minus 1 comma 0 all right so we
got the well of this point that is
nearly 1 comma 0 right now we need to
find out the value of this point what is
the value of this point Q right find
this color is the best right so see your
friend if you want to do with the
section formula that is 2 ratio 1 also
it is also right and if you want to do
this here see a P and Q right so you
have PQ is equals to Q B so I can say
that's the point Q is the midpoint of
this a v-line right sorry PQ line and
while you see this this much right only
see this much here this Q point is the
midpoint of the pv line also because
this part is equals to this part so I
can use the section formula as I used to
do or III really do here I just do it
like this or I can use also here the
midpoint formula right so I think
midpoint formula is the best for here
right midpoint formula is just the
average of this two points right the
middle point right so let me use here
meet one from now that is X 2 it is X 2
let me write properly ok the Q point
that is X 2 comma Y 2 is equals to write
meatman form up and here X 1 plus X 2
open to again y 1 plus y 2 open to write
or we can say that just average of these
P points so average of x coordinate that
is minus 1 plus write minus 1 and this
minus have an average of this
x-coordinate that is negative 1 plus
minus negative 7 whole divided by 2 and
again y 1 plus y 2 or the average of
this 0 + 4 that is 0 plus 4 divided by 2
right so it will be minus so minus 1
plus minus minus 7 up in - 4 upon -
right sweetie will be minus 8 I want to
again for upon - that is - right so over
what we guard that the cue point is
equals to minus 4 comma 2 right so we
got the value here that is minus 4 comma
2 so we got the answer here that near
the line was a B and the pool two points
here P and Q was try acting this line so
P point we got that is minus 1 0 and the
Q point is minus 4 comma 2 so like this
we have to solve this kinds of problem
all right either the line is dividing
into four equal parts or five equal
parts or seven equal parts we just have
to first find out the ratio in which
ratio the points are being cut right so
once we get this all well we can easily
apply the section formula or the
midpoint formula according to the
situation and get the value right so
we'll the meeting in the next video with
a different type of problem in Section
four malarkey bye bye for now