Class 10 Exam > Class 10 Videos > Examples: Coordinate Geometry- 1
Examples: Coordinate Geometry- 1 Video Lecture - Class 10
FAQs on Examples: Coordinate Geometry- 1 Video Lecture - Class 10
| 1. What is coordinate geometry? |  |
Ans. Coordinate geometry is a branch of mathematics that deals with the study of geometric figures using a coordinate system. It involves representing points, lines, curves, and shapes on a plane using numerical values called coordinates.
| 2. How do you find the distance between two points using coordinate geometry? | |
Ans. To find the distance between two points using coordinate geometry, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2], where (x1, y1) and (x2, y2) are the coordinates of the two points.
| 3. What is the midpoint formula in coordinate geometry? | |
Ans. The midpoint formula is used to find the coordinates of the midpoint between two given points. It is given by:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2], where (x1, y1) and (x2, y2) are the coordinates of the two points.
| 4. How can we determine if three points are collinear using coordinate geometry? | |
Ans. Three points are collinear if the slope of the line connecting any two points is the same as the slope of the line connecting the other two points. In coordinate geometry, you can calculate the slope between two points using the formula:
Slope = (y2 - y1)/(x2 - x1). If the slopes of all three pairs of points are equal, then the points are collinear.
| 5. How can we find the equation of a line in coordinate geometry? | |
Ans. To find the equation of a line in coordinate geometry, you need to know either the slope of the line and a point on the line or two points on the line. If you have the slope and a point, you can use the point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. If you have two points, you can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).
Text Transcript from Video
hello friends this video on coordinate
geometry part 15 is brought you by exam
fear calm no more fear from exam before
watching this video please make sure
that you have watched part 1 to part 14
let's take home example let the opposite
angle point of a square be 3/4 minus 1
by a minus 1 we have to find the
coordinate or the remaining slip string
square actually here made rectangle it
has to be square this is square and the
points are 3/4 1 minus 1 we have to find
according to the other forms let this be
X 1 and at this point B a right now to
get into equation first thing is AP is
equal to BC first is a B square is equal
to P Square will be everything in square
form second if you mean it is AC square
is equal to VA square plus BC square
this right triangle this curve is there
so here you get two equations so we get
two equation we can solve and we can get
this and do some fun I am NOT doing the
complete thing so first find a v square
a B square is nothing but X minus 3
square plus y minus mu star correct EB
square X minus 3 square minus Q square
is equal to P Square D XI square is what
this one X minus y y minus minus 1
square there is X minus 1 square plus y
plus expand this we get X square plus 9
minus
x plus y squared plus 16 minus 8x is
equal to x squared plus 1 minus 2x plus
y squared plus 4 plus 4x X square Y
square X square by spot cancer website
so what we get is this side being in
minus X X - 6 y 8 YX think there's a
minus 2 X so this becomes minus 6x plus
2x is minus 4 X X part bond then minus
8y minus 4y all right for y and minus V
1 is y plus 1 X so y square plus 2 plus
2 so minus 8y minus 12 is minus 10 y y
part is can send the remaining thing is
9 9 + 16 25 25 - 124
- 23 verse 23 is equal to 0 for big 8 X
is nothing but 23 minus 1 so I got this
equation X in terms of Y also we have
another equation this one G square equal
to P Square will be C square so if you
saw this in this efficient if we make a
C square is nothing but 3 t minus 1
square because a and C 3 in 1 plus 4 - -
from this 4 plus 4 square this is AC
square this is equal to VB square plus
BC square in a square you know is
nothing but X -3 squared plus y minus mu
star and B square is nothing but X minus
1 square
by Versalles and they all equal it you
saw all these equation now this is in
terms of X in mind also we haven't
written it anyway you will get the value
of x to weigh in prior May 1 will get X
is 9 by 2 or minus 1 by 2 and y is 1 by
20 this is as you let seemed to solve
which let's say for my example the
question says PQRS the four points in
the plane we have to do that
PQ R is a rhombus not L square so if all
four sides are equal it can be either on
the square but if all four sides are
equal and the diagonals are also equals
n square diagonals are not equal but
force I say put then it impose this kind
of pushing here with them actually what
we can do here just keep the approach
zero so so this is the my any
quadrilateral EQ others you have this
point two minus 1 3 4 minus 2 e 3 and
now what do you get the waves you can
try to find the value of p QQ r RS and
PS all sides eq q r RS and SP you will
find that all sides are equal
you can augment your formula this is
number this will be n Q root 3 minus 2
square plus 4 minus minus principal like
this you can find the distance then also
you find them diagonally then you find
that
er is not equal to us so that I are not
equal you say that sides are equal
diagonally across that means it is a
rhombus that is that motion followed in
trials we have to find the coordinates
of the center of the circle passing
through 0 1 0 minus 2 1 and minus 3
commodity also we have to find the
videos I'll explain what polar is same
in this circle actually and this passes
through 0 0
- 2 1 and minus 3 for my three points we
have to find a center center that
supposes 0o they defined the center also
you've defined the radius so let's give
this name a B and C these points so the
radius is nothing but weight and there
is a will be a nose all right equal so
we can say the radius square is also
equal to a is Philo this Farrow system
so then what we can do is we can find
this again we'll have secretions and
solves equations to get the value of x
in my example this means x + y ou a
square is nothing but right OH
a square is nothing but X minus 0
squared plus y minus 0 square plus X
square plus 1 similarly OC square is
nothing but X plus 3 square plus y minus
2 R is nothing but X square plus 9 plus
X plus y square plus 4 minus similarly
OB square is nothing but X plus Q square
plus y minus 1 square
there is nothing but X square plus 4
plus 4 y plus y square plus 1 minus 2 1
all right now you can equate this Oh a
squares below C square suppose we do
that we'll get X square plus y square is
equal to X square plus 9 plus 6x plus y
square plus or minus 4 what X by Y
square cancel so what we get in this
case is C
X minus 4y plus 13 is it a fish number
one it's really gonna quit
Oh a square and ob square Y because X
square Y square I will get cancelled so
we'll do that we'll get the x squared
plus y squared 3 squared is equal to x
squared plus 4 plus 4 y plus y square
plus 1 minus 2y little movie square
equity my way square v square X by Y
square cancel so what we get is is X 4x
minus 2y plus 5z this we have to
equation in x and y right 6x minus y
plus 13 is equal to 0 and 4x minus 2i
plus 5 is equal to 0 you multiply with
this 50 we will get 4 by 4 by you cancel
can solve this equation you solve this
equation
you'll get what text is equal to Q by 2
and Y is equal to 11 by once we get this
you can find the radius from Z you can
find the radius radius is nothing but
we'll don't expect this mess with
hitting anything o a-square b-square
anything this is nothing but root of T
by mu squared plus 11 by 2 and this
comes out to be 1 by X minus then
sympathy I'm taking this point XY here 3
points you got two equations solved it
you got the value of XY and T for 3 you
have to prove the add points or these
are the points at the points for the
parallelogram and the question is asked
this is a rectangle or not she had two
ways to solve this question one is for
sleeping tall this is important to leave
UCD so if you can find a V on the sides
all the sides and we see the opposite
sides are equal then it can be either
parallelogram or rectangle then you find
this diagonals a diagnosed or equal that
is rectangle it does not equal it is
parallelogram
so one that is one approach we find all
the sides and we find both diagonals and
then we can tell whether it is a
parallelogram or a ten second one easy
approach we have is since you already
know the formula to find the midpoint so
we have this ABC we can find the
midpoint so the midpoint of AC and the
midpoint of BD are coinciding there's
same point that means it has to be
either parallelogram all the time but
definitely not take the side that leaves
and then we can check all ABN easy okay
if a B in AC are different that means it
is a telegram if they are saying that is
it's a good time correct so I'll write
PV C once points is the different
approach saw this is minus minus 2 minus
1 B is 1 for my 0 is 1 per month right
let's say make the point of easy for
plus minus 2 or plus minus 2 by 2 or ma
c plus minus or better please the
smallness in been correct comes out to
be 1 comma 1 similarly midpoint of vidi
vici should be 1 plus 1 by 2 and 2 plus
0 by 2 that will also be 1 comma since
the midpoint of V dnase here coinciding
that means it is either rectangle or
that way around now to prove it is the
parallelogram we had to find them along
AC and we need if they are same
rectangle it not there well they see
people do nothing but four minus minus
two squared plus three minus minus one
squared correct this is nothing but
you'll go 6 squared is 36 plus 4 spread
that is 16 right this is the D word dude
off you see we'll need to find reading
we need nothing but Rudolph it says 1
minus 1 1 minus 1 square plus n minus 2
square
all right this becomes 0 square plus 8
squared is 64 and this is nothing but
root 64 so if you see both are not
saying they are not same so it is not
rectangular there's very little all
right so in this case we didn't find a
BBC CD and the we just found the
midpoint and record our midpoint of cool
side thank you
visit exam viacom to watch free
education videos try free online test
get the best quality study materials
study from the best tutors and mentors
and mushroom thanks the screen
geometry part 15 is brought you by exam
fear calm no more fear from exam before
watching this video please make sure
that you have watched part 1 to part 14
let's take home example let the opposite
angle point of a square be 3/4 minus 1
by a minus 1 we have to find the
coordinate or the remaining slip string
square actually here made rectangle it
has to be square this is square and the
points are 3/4 1 minus 1 we have to find
according to the other forms let this be
X 1 and at this point B a right now to
get into equation first thing is AP is
equal to BC first is a B square is equal
to P Square will be everything in square
form second if you mean it is AC square
is equal to VA square plus BC square
this right triangle this curve is there
so here you get two equations so we get
two equation we can solve and we can get
this and do some fun I am NOT doing the
complete thing so first find a v square
a B square is nothing but X minus 3
square plus y minus mu star correct EB
square X minus 3 square minus Q square
is equal to P Square D XI square is what
this one X minus y y minus minus 1
square there is X minus 1 square plus y
plus expand this we get X square plus 9
minus
x plus y squared plus 16 minus 8x is
equal to x squared plus 1 minus 2x plus
y squared plus 4 plus 4x X square Y
square X square by spot cancer website
so what we get is this side being in
minus X X - 6 y 8 YX think there's a
minus 2 X so this becomes minus 6x plus
2x is minus 4 X X part bond then minus
8y minus 4y all right for y and minus V
1 is y plus 1 X so y square plus 2 plus
2 so minus 8y minus 12 is minus 10 y y
part is can send the remaining thing is
9 9 + 16 25 25 - 124
- 23 verse 23 is equal to 0 for big 8 X
is nothing but 23 minus 1 so I got this
equation X in terms of Y also we have
another equation this one G square equal
to P Square will be C square so if you
saw this in this efficient if we make a
C square is nothing but 3 t minus 1
square because a and C 3 in 1 plus 4 - -
from this 4 plus 4 square this is AC
square this is equal to VB square plus
BC square in a square you know is
nothing but X -3 squared plus y minus mu
star and B square is nothing but X minus
1 square
by Versalles and they all equal it you
saw all these equation now this is in
terms of X in mind also we haven't
written it anyway you will get the value
of x to weigh in prior May 1 will get X
is 9 by 2 or minus 1 by 2 and y is 1 by
20 this is as you let seemed to solve
which let's say for my example the
question says PQRS the four points in
the plane we have to do that
PQ R is a rhombus not L square so if all
four sides are equal it can be either on
the square but if all four sides are
equal and the diagonals are also equals
n square diagonals are not equal but
force I say put then it impose this kind
of pushing here with them actually what
we can do here just keep the approach
zero so so this is the my any
quadrilateral EQ others you have this
point two minus 1 3 4 minus 2 e 3 and
now what do you get the waves you can
try to find the value of p QQ r RS and
PS all sides eq q r RS and SP you will
find that all sides are equal
you can augment your formula this is
number this will be n Q root 3 minus 2
square plus 4 minus minus principal like
this you can find the distance then also
you find them diagonally then you find
that
er is not equal to us so that I are not
equal you say that sides are equal
diagonally across that means it is a
rhombus that is that motion followed in
trials we have to find the coordinates
of the center of the circle passing
through 0 1 0 minus 2 1 and minus 3
commodity also we have to find the
videos I'll explain what polar is same
in this circle actually and this passes
through 0 0
- 2 1 and minus 3 for my three points we
have to find a center center that
supposes 0o they defined the center also
you've defined the radius so let's give
this name a B and C these points so the
radius is nothing but weight and there
is a will be a nose all right equal so
we can say the radius square is also
equal to a is Philo this Farrow system
so then what we can do is we can find
this again we'll have secretions and
solves equations to get the value of x
in my example this means x + y ou a
square is nothing but right OH
a square is nothing but X minus 0
squared plus y minus 0 square plus X
square plus 1 similarly OC square is
nothing but X plus 3 square plus y minus
2 R is nothing but X square plus 9 plus
X plus y square plus 4 minus similarly
OB square is nothing but X plus Q square
plus y minus 1 square
there is nothing but X square plus 4
plus 4 y plus y square plus 1 minus 2 1
all right now you can equate this Oh a
squares below C square suppose we do
that we'll get X square plus y square is
equal to X square plus 9 plus 6x plus y
square plus or minus 4 what X by Y
square cancel so what we get in this
case is C
X minus 4y plus 13 is it a fish number
one it's really gonna quit
Oh a square and ob square Y because X
square Y square I will get cancelled so
we'll do that we'll get the x squared
plus y squared 3 squared is equal to x
squared plus 4 plus 4 y plus y square
plus 1 minus 2y little movie square
equity my way square v square X by Y
square cancel so what we get is is X 4x
minus 2y plus 5z this we have to
equation in x and y right 6x minus y
plus 13 is equal to 0 and 4x minus 2i
plus 5 is equal to 0 you multiply with
this 50 we will get 4 by 4 by you cancel
can solve this equation you solve this
equation
you'll get what text is equal to Q by 2
and Y is equal to 11 by once we get this
you can find the radius from Z you can
find the radius radius is nothing but
we'll don't expect this mess with
hitting anything o a-square b-square
anything this is nothing but root of T
by mu squared plus 11 by 2 and this
comes out to be 1 by X minus then
sympathy I'm taking this point XY here 3
points you got two equations solved it
you got the value of XY and T for 3 you
have to prove the add points or these
are the points at the points for the
parallelogram and the question is asked
this is a rectangle or not she had two
ways to solve this question one is for
sleeping tall this is important to leave
UCD so if you can find a V on the sides
all the sides and we see the opposite
sides are equal then it can be either
parallelogram or rectangle then you find
this diagonals a diagnosed or equal that
is rectangle it does not equal it is
parallelogram
so one that is one approach we find all
the sides and we find both diagonals and
then we can tell whether it is a
parallelogram or a ten second one easy
approach we have is since you already
know the formula to find the midpoint so
we have this ABC we can find the
midpoint so the midpoint of AC and the
midpoint of BD are coinciding there's
same point that means it has to be
either parallelogram all the time but
definitely not take the side that leaves
and then we can check all ABN easy okay
if a B in AC are different that means it
is a telegram if they are saying that is
it's a good time correct so I'll write
PV C once points is the different
approach saw this is minus minus 2 minus
1 B is 1 for my 0 is 1 per month right
let's say make the point of easy for
plus minus 2 or plus minus 2 by 2 or ma
c plus minus or better please the
smallness in been correct comes out to
be 1 comma 1 similarly midpoint of vidi
vici should be 1 plus 1 by 2 and 2 plus
0 by 2 that will also be 1 comma since
the midpoint of V dnase here coinciding
that means it is either rectangle or
that way around now to prove it is the
parallelogram we had to find them along
AC and we need if they are same
rectangle it not there well they see
people do nothing but four minus minus
two squared plus three minus minus one
squared correct this is nothing but
you'll go 6 squared is 36 plus 4 spread
that is 16 right this is the D word dude
off you see we'll need to find reading
we need nothing but Rudolph it says 1
minus 1 1 minus 1 square plus n minus 2
square
all right this becomes 0 square plus 8
squared is 64 and this is nothing but
root 64 so if you see both are not
saying they are not same so it is not
rectangular there's very little all
right so in this case we didn't find a
BBC CD and the we just found the
midpoint and record our midpoint of cool
side thank you
visit exam viacom to watch free
education videos try free online test
get the best quality study materials
study from the best tutors and mentors
and mushroom thanks the screen
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Nov 23, 2024 Last updated |
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