Find Area of Triangle - Coordinate Geometry Video Lecture - Class 9

now let's find the area of the triangle
whose vertices are a 3-2 be 11 8 and c8
12 all right here to find the area of
this we have two methods I told you
already
first one we have discussed in the
previous video and the second one I
haven't that's a shortcut so try to see
the entire video right let me let me
write here our triangle suppose this is
our triangle okay and this is a which is
3 2 and this is B which is 11 comma 8
and this is C which is 8 comma 12 okay
so let me suppose I'm just supposing
this is our x1 comma y1 and this will
working as a x2 comma y2 and suppose
this is working as a x3 comma Y 3 so to
find the area of the triangle I told you
we can use simply the formula of that
triangle
alright so area of the triangle area of
triangle ABC if you know the formula
just to write here the formula but if
you don't know then still we have a
trick I told you all right always we
need to follow
1 2 3 ratio 1 2 3 and after that 2 3 1
and then 1 2 now 3 1 2 all right
always 1 2 3 2 3 1 and then 3 1 2 you
know just we have this way now this is
representing X and this is root any Y
you know this ok so first one when X is
1 right when X is 1 Y will be Y 2 minus
y 3 so it will be Y 2 minus y 3 and plus
again when X will be 2 y will be Y 3
minus y 1 all right so when X will be 2
it will be Y 3 minus y 1 ok and now when
x will be 3 y will be y 1 minus y 2 all
right so when X will be 3 it will be Y 1
minus y 2 all right it's a little space
ok I hope you understand this all right
so now let's put all the values so 1 by
2 so here we have already suppose x1 y1
x2 y2 and x3 y3 so when
x1 why is our X 1 that is 3 so when it
is 3 another will be Y 2 minus y 3 that
is 8 minus 12 all right
8 minus 12 and then when X 2 so our x2
easier 11 all right so 11 then it will
away 3 minus y1 so what is our Y 3 y 3
is 12 y 3 minus y 1 there is 2 so it
will be 12 minus 2 and then X 3 so what
is our X 3 X 3 is our 8 so when it is 8
it will be Y 1 minus y 2 our y1 is 2 and
Y 2 is 8 so it will be 2 minus 8 all
right so now 1 by 2 now 3 times this 8
minus 12
that's minus 4 and this is 11 and then
12 minus 2 that is 10 and this is 8 and
then 2 minus 8 that is minus 6 so 1 by 2
all right
3 minus 4 that's minus 12 and then it is
110 and it's 8 6a minus 48 it will be
right minus 48
so now minus 48 n minus 12 minus 60 and
110 so it will be 50 so all right 1 by 2
times 50 so it's absolute sign all right
whether it is negative or positive
always will be writing positive because
area of the triangle will be always and
always positive so 2 times 25 so 25 unit
square is the area of the triangle all
right this is how we need to find out by
using formula and by another method I'm
going to do see I'm goin other-- method
is very easy I'm going to just tell you
here area of triangle suppose Delta area
this this triangle is representing area
of the triangle then write like this x1
y1 x2 y2 and then x3 y3 this is your
alright and again repeat this last part
one more time here okay this is not last
the first part I'm sorry all right
x1 y1 and after that we have a formula
the triangles formula is 1 by 2
southeast - southwest all right this is
the formula so what is south east and
south
I'm making arrows MC I'm making south
like in the north Lexia this is
representing north south you know this
is east and this is waist so I'm making
southeast arrows like this all our
southeast arrows alright so first the
area is 1 by 2 all right so it will be
now X 1 y 2 plus in the bracket again
take and then X 2 alright y 3 and then X
3 y 1
I took X 1 y 2 plus X 2 y 3 plus X 3 y 1
alright and then - now we deal with this
Southeast now let's deal with Southwest
Southwest means this part all right so
this one all with the green color so it
will be now x2 y1 all right x2 y1 and
then plus X 3 y 2 X 3 y 2 and then plus
X 1 Y 3 X 1 Y 3 alright this is the
another method I was talking about if
you do practice this will be really very
easier right so let me do with this
method so one by two
first I'm gonna represent in the same
way alright so what is my x1 y1 x2 y2
all I'm gonna write alright so what's my
first x1 y1 that's three two and then
it's 11 8 and then we have 8 12 and I
say that one more time I need to repeat
this first one that's three two okay so
now see how easy it's gonna be 1 by 2
first I'm going to do all the southeast
alright this one so now see first 3 into
8 3 into 8 plus 11 into 12 11 into 12
and then 8 into 2 all right
8 into 2 alright and then minus all the
southwest this one so 11 into - alright
11 into 2 and then Plus this 8 into 8
all right
8 into 8 and then plus these three into
12 3 into 12 all right so now let's add
see 3 times 8 that is 24 11 times 12
that's going to be 132 and then 8 into 2
that's going to be 16 - now 11 times 2
that is 22 8 times 8 that is 64 and then
3 times 12 that is 36 all right so 1 by
2 now add this this is going to be 172 -
now let's add this part this is going to
be 122 all right and 1 by 2 172 - 122
that will be 50 all right and then 2
times 25 so again here we got that
answer twenty five 25 units square all
right unit is squared because it's area
so this is how we need to solve you know
using this trick as well as the normal
this formula this is a little bit faster
you know if you practice better
you need just a practiced first to write
southeast south southeast and then
Southwest Southwest southeast it's it's
going to be easy I'll do one two or more
problems and that will give you more
practice and more concept all right
catch you the next play goodbye