Examples (NCERT): Point Slope Form Video Lecture | Mathematics for Airmen Group X - Airforce X Y / Indian Navy SSR

hello friends this video straight line
part 7 is brought to you by exam fear
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watching this video please make sure
that you have watched great line part 1
to part 6 you have to prove that that
this is a line X plus B by plus YZ will
draw and prog line this is the line X
plus dy plus there is a line which is
parallel to this line and it will pass
this through x1 y1 passes through this
point X and comma now we have to prove
that this is first Elven in this is a
way we have to prove that this is the
equation of line in E X minus x1 plus B
Y minus 5 minutes now since both the
lines are parallel
first let's find the slope of line in
slope of line negative will be produced
above lines element because we got panel
now let's find the slope of line every
LM first this is K X plus V y plus Z is
equal to 0 you can rewrite this equation
as B Y is going to minus ax minus C or
we can say Y is equal to minus a by B X
minus C by B what I've done I have
divided this equation by B both left
side right hand side if you compare this
equation with Y is equal to MX plus C
then we can say that or this equation M
is equal to minus a by but is what you
are looking for you have got the value
of M M is equal to minus D by B now if
you have the value of M is equal to
minus a by B that is slope of line album
since L 1 is parallel to L 2 we can say
that M - a - M 2 for the lines of
violence the spokes are equal therefore
slope of line at two there is M mm equal
to minus K by now for the line L 2 we
have slope and we have
two points so we can this formulate this
equation the equation is y minus y
naught is going to M into X minus 16
this is the equation of line into for
line enter this is the equation or we
can say y minus y1 is equal to M is
nothing but minus K by V into X minus x1
correct now this is nothing but V into y
minus y1 plus a into X minus sorry X
minus x1 is a variance and that is what
we are asked to so we have proved that a
into X minus x1 plus B into y minus 1
that is going to be very simple in in
all the cases when you get questions on
lines you first draw the diagram here we
do X could be well perceivable is room
is a line hello
then we drew one more line parallel to
line this because if I told them you
have to find the equation of line which
is parallel to like this so they drew
one more line is parallel line element
and we know that this is the point x2
environment that is passing through the
line Headly then we solve this once you
sword once you draw the diagram of the
line you get a clearer picture of what
you are expected to do and how to
approach so the first thing when you get
any problem in the lines the first thing
you should do is that you should draw
the graph not the exact graph that is
not required you should not draw the
full coordinates and keep what sharding
the points you can just draw a front
graph and then you can approach them
problem so the first step is draw the
graph and then understand the problem
here so we clear the graph and we got a
clear understanding of the problem and
then we solve them
let's take for example it is little
tricky so it says that vertices of angle
triangle PQR are 2 comma 1 minus 2 comma
3 and 4 comma 5 we have to find the
equation of median through what
our first let's draw the triangle this
is our triangle PQR P Q and R so it says
P is equal to 2 comma 1 Q is good to say
minus 2 comma 3 and R is equal to 4
comma 5 now we had to order you to find
the equation of median through vertex R
so from our we are going to draw a
minion so that means we'll draw a line
from R to let suppose this is s and here
these two sides are equal that this Q is
is equal to PS this is median now let
draw this line which connects R and s
this is the line which connects our NS
so we have to find the equation of line
s r9 s sir this is my del let me this is
the triangle PQR the vertices are given
and you to find the equation of median
through vertex are from R this is the
median this divides a slightly to to be
thorough so coordinates of X we can say
that will be to this coordinates of P
let's say s the video feed us Q by dou Y
because s is the midpoint even if we go
by formula M by n where m and n are one
by one will get the same value so s will
be P plus Q by 2 since s is the midpoint
so we will say s of X will be 2 minus 2
by 2 that is 0 and s of Y is equal to 1
plus 3 by 2 is equal to 3 so we have s
of X that is 2 minus 2 we add this 2 by
2 in SFI so we have this value this is
two-zero c'mon now it is very simple for
us we know two points and we have to
find the equation let's find the slope
of line SR that is nothing but L is
equal to y2 minus y1 by x2 minus XP so
here let's assume this is y 2 and this
is y 1 so this becomes Phi minus 2 by 4
minus 0 that is 3 by 4 now equation of
the line will be y minus 2 by X minus
zero is button 3 by this will be the
equation of line or we can say 4y minus
8 is equal to KX or we can say 3x minus
4y plus 8 is equal this is the equation
of the line SR so equation of the line s
l's
3x minus 4y plus 8 is equal to what we
have done we have plotted the triangle
and then we have found the value of
coordinates of X s is nothing but t plus
Q by 2 so we have found has to be 0 and
2 we now know the point s and R and we
have this on the equation this problem
says that we have to find the equation
of the line which passes through minus 3
and 5 and this perpendicular to the line
that passes through 2 5 and minus 3
comma 6 draw a line first let's suppose
this is a line and let's suppose that
this is 2 5 and minus 3 6 C whatever
points I am putting here it will not
come into use the actual XY graphs just
to explain you guys I am using these
points what I am told is there is a line
is perpendicular this will draw
perpendicular
this is the line perpetrated upon and
there's a point here that this minus
three comma Y and we have to find the
equation of this life correct so this is
l1 and let's suppose this is empty and
we have to find ll not anything first we
let it find the slope of know what is
the approach the approaches we have been
given one point so if we if you manage
to find the slope of this line l1 or if
you find one more point then we can
solve the equation
I just know or one more point in this
equation square norm we know that since
Alvin is perpendicular to L do we know
the slope of n2 so we can very easily
find the slope of a line and then when
we will have slope of element and then
we'll have a more point in L then we can
easily get the equation let's try this
first let's find the slope of negative
and that is m2 that is nothing but again
y2 minus y1 by x2 minus x1 so in this
case it will become 5 minus 6 by 2 minus
minus 3 that is minus 1 by 5 this is the
snowball m2 now MN into m2 is equal to
minus 1 we know this is slope of L M 1
the slope of line and since these two
are parallel perpendicular the product
of this close is minus 1 so m1 is equal
to minus 1 by M 2 is equal to minus 1 by
minus 1 by 5 this becomes 5 so slope of
M 1 is equal to 5 now we have slope of M
1 is equal to 5 and we have two points
or one point in line that is minus TFI
so we can say the equation of this line
is y minus Phi by X plus three minus
three and five is gear is equal to five
this is the equation because why - why -
why not by X minus X bar is going to M
this equation we know this is the
equation the line this becomes y minus 5
is equal to 5x plus 50 or we can say by
- or against it
5x or we can write in this form I exist
5x minus y plus 20 is equal to this is
the equation of line l1 that's what we
are supposed to find what do they oppose
we followed we went told that there is a
point in it
and you do and we were supposed to find
the equation of line element but since
we were not aware of any other thing we
wanted to know the slope also of l1 to
get the equation we knew the slope of L
2 and we knew that element two are
perpendicular so we found the slope of L
1 now once we had slope of L 1 we got
the equation of line thank you
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