Example : Sectional Formula - Coordinate Geometry Video Lecture - Class 10

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my example the question says is one
permit rules for gamma Y X comma 6 MC
comma five R vertices of parallelogram
taken in order we have to find the value
of x n 1 so let's draw the parallelogram
ABCD inside and the point try the order
so let's go this is 1 2 so for y since X
6 and this is correct
a/c now since their parallelogram you
see the diagonals will meet at this one
so let's the midpoint vo so all will be
the midpoint of AC and we will also be
midpoint of BD because it is a
parallelogram we know that o is the
midpoint of AC you know we lost be the
midpoint of BD so we'll find the
midpoint of CAC and we'll find the
midpoint of VD will be same so we'll say
midpoint of BC this will be a and C find
a mcpoyle this X this is 1 X plus 1 by 2
it's just 6 this is 2 that is 6 plus
provided similarly made the point of VD
is equal to this is equal to 4/3 this
fourth plus 3 by 3 this is why you don't
want this point this is 5 it is why
gloves - and both are equal both this
points are equal actually both this
points are both both are equal and both
are equal to 4 still will make
they're equals we can say that first
thing is computing the XX partnering
interval this becomes X plus 1 by 2
becomes 4 plus 3 by 2 to cancel so we'll
get X is equal to 4 plus 3 minus 1 that
is 6 first part done since this is also
equals we'll compute the y part we'll
get 6 plus 2 where 2 is equal to BI plus
5x2 cancel so we get Y is equal to 6
plus 2 it is 8 minus 5 like this so we
got eggs and we got what so this is
nothing but X is 6 and this very nothing
but correct plus we have found the value
of a very simple since it is
parallelogram we know that the diagonals
are midpoint of the intersection point
and Wagnalls our midpoint of AC and E
and with this information we found the
value of x and let's take an example
find the coordinates of a point a with a
V is the diameter of the circle whose
Center is 2 comma minus 3 and V is 1 4
ma draw a circle this is a circle maybe
is the diameter of the circle this is a
point Center AV the diameter of the
circle where V is given 1 comma 4 this
point and centre is no comma minus this
is also given we have to find the value
of point a let this be X memo we know
that this point O is the midpoint of a
be correct
we know that Oh a is midpoint of a B so
we can say that if you compute the next
part the midpoint of a B is nothing but
X plus 1 by 2 X 14 I'm saying
x-coordinate of midpoint of V V is the
keyword X 1 by 2 and that is two given
so you get X is equal to 4 minus 1 that
M
so you gotta excellent okay similarly
midpoint of a B the y coordinate is
nothing but this is y is for y plus 5 2
and this value is -3 given - thing or Y
is equal to minus 3 into 2 is minus 6
minus 4 this is minus 10 so Y is equal
to minus T so you got x + y x + y is
nothing but 3 comma minus 10 and these
are the coordinates of point a and that
is my answer
very simple you draw that I am you have
this point V you have fine hole at a
point Li and we do we know that o is the
midpoint of e will take up example the
question say is if a and B are -2 minus
2 n 2 - 4 respectively find the
coordinates of P such that ap is equal
to 3 by 7 a B and P lines on the line
segment people
so let's first draw this if this is a
this is B this is minus 2 minus 2 and
this is 2 comma minus 4 this is a B and
there is a point P that lines like other
line segment a B is this point P and the
question says that a P is equal to 3 by
7 PP sorry that is a P is equal to 3 by
it 780 or we can say that a B by a P is
equal to 3 by 7 you know that what we
have to find is AP by P B so a little
break actually
you break this what we'll do AP will
write as a three by a B is nothing but a
P plus P using
this is what right does if you see the
whole thing is in the form of a PN P we
take a reciprocal big-eared AP plus P V
by a P is equal to 7 by 3 or again a V
by AP + e V by V Google - 7 by 3 this is
1 equity so we'll get P B by a pianist
to speak we speak
this P is equal to 7 by 3 minus 1 and
that is nothing but full byte so PBY AP
is 4 by 3 therefore a P by P is 3 5 this
was the most difficult part action so
when we got a p YB v is equal to 3/5 for
our colonists on there is a normal
portion where the ratio is given an ear
defined another point the logic here was
AP by AV was given and then we found AP
by AP by EB was given live on AP by P if
you want ain't give us C by not very
simple you take this point you multiply
with this you take this you multiply
with this so I say P of X is nothing but
3 into 2 into 2 plus 4 into minus 2 4
into minus 2/3 plus means awesome
all right that comes out to be 6 minus 8
by 7 that is minus 2 by saying P of Y is
nothing but 3 of minus 1 3 into minus 4
plus 4 into minus 2 over into minus 2 by
3 plus 4 that is minus 12 minus 8 by 7
because -91 is set so we have got this
point V as minus 2 by 7 and minus 20 by
7 and that is erased very simple let us
take one more example here to find the
coordinates at the point which divides a
line segment joining a minus 2 power to
be 2 comma 8 into 4 equal
I will not solve this question let's
tell you the approach how to solve this
question this is point a this is point B
minus 2 comma 2 and this is 2 comma 4
equal parts so we will divide into four
equal parts 1 2 to give you all equal
parts if this length is K this is K this
is K all are key and at this point we
see D any of the points so if you see
this point C SEPA divide this line
segment a into K by 3 K because this
side is left that is K and right-hand
side is 3 K so C will divide C will
divide in the form of K by 3 K that is 1
by 3 right 1 right similarly D for D you
see this side 2 K this side ok so for D
dy today or against a 1 by 1 or e this
side is 3 K this side escape for e will
be 3 K by K that is 3 is 2 1 all right
so D is 1 is to 1 and he is 3 is to 1 so
we have all this we have these 3 points
and we know the ratio in which it
divides there isn't but long we for
example we take this point C 4 if you
want to find the value of point C I will
take this point a this point B and we
point C you know the coordinate of the
point a and V 2 and minus 10 s 2 and 2
or B we have to n8 and horse even a
ratio is monastery we can very well find
them Point C will take 3 we multiply
this will take 100 left
similarly for point D same thing this is
- - - and this is to aid because a this
is B and for D I know the ratio is 1 is
to 1 so I'll find this is the midpoint
actually you'll find about d.c where
every of the same thing will do this is
a this is B these two 1/8 and a is minus
2 comma minus -2 power plus 2 and we
have this point E and the ratio which is
divided his trays to 1 I have this ratio
I have the points I can find of a lower
point keep very simple let's take up
example find the area of rhombus if the
vertices are 3 0 4 5 - 1 4 minus 1 minus
minus 1 actually this question is gone
for section formula this question is
only for the distance form leg so in
Norma's we know it is a rhombus Ashley
the diagonals are perpendicular exactly
perpendicular in d.c since the diagonals
are perpendicular you take the area is
nothing but 1 by 2 into AC beauty this
value of the rhombus 1 by 2 into fret of
magnets so this is a V this is C this is
D so you are divided 1 by 2 into AC into
VD let's find this is AC so AC is
nothing we're good off taking this end
this so 3 minus minus 1 square plus 0 +
4 0 minus 4 spur this becomes root off 4
square plus minus 4 where there is root
of 16 plus 16 that is 4 root correct
let's find the value of reading it is
nothing but rule of this
fine for and minus 2 that is 4 minus
minus 2 square plus 5 and minus 1 so 5
minus minus 1 square this becomes
nothing but 6 square plus 6 square
correct the dense fog
check the 6 plus 36 is 26 riveting so we
have 8 AC and we have reading so you
find the area it is nothing but 1 by 2
into AC DVD because nothing but 1 by 2
into 4 root 2 into 36 you to do to do to
cancel so the comfort is 6 into 4 sorry
this is 4 for 650 for the 6 into 4 that
is 24 and kuna does not even so same
unit Square and that is massive that is
it will we just found a C in Part B D
and I found the area to be 1 by 2 in
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