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Coordinate Geometry (Introduction & Examples) - Quantitative Aptitude Video Lecture | Quantitative Aptitude (Quant) - CAT
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FAQs on Coordinate Geometry (Introduction & Examples) - Quantitative Aptitude Video Lecture - Quantitative Aptitude (Quant) - CAT
| 1. What is coordinate geometry? |  |
Ans. Coordinate geometry is a branch of mathematics that deals with the study of geometric figures using coordinates. It combines algebraic techniques and geometric concepts to analyze shapes and their properties on a coordinate plane.
| 2. How do you find the distance between two points in coordinate geometry? | |
Ans. To find the distance between two points in coordinate geometry, you can use the distance formula. The formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
| 3. How do you find the midpoint of a line segment in coordinate geometry? | |
Ans. The midpoint of a line segment in coordinate geometry can be found by using the midpoint formula. The formula is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
| 4. What is the slope of a line in coordinate geometry? | |
Ans. The slope of a line in coordinate geometry represents its steepness or incline. It is calculated by dividing the change in y-coordinates (vertical distance) by the change in x-coordinates (horizontal distance) between two points on the line. The formula for finding the slope is:
Slope = (y2 - y1)/(x2 - x1)
Where (x1, y1) and (x2, y2) are two points on the line.
| 5. How do you determine if two lines are parallel in coordinate geometry? | |
Ans. Two lines in coordinate geometry are parallel if their slopes are equal. If the slopes of two lines are the same, their lines will never intersect and are considered parallel.
Text Transcript from Video
welcome to the video my name is push
winterkill so we're going ahead to learn
the basic concept of the general
equation of a line this is the first
video for coordinate geometry so my name
is Chris bender Gill and this here is my
email address it's pushpin to 0-8 at
gmail.com don't forget to contact me or
give your valuable feedback and do not
forget to Like us on Facebook the
Facebook link would be on our channel
page right so let's just go ahead and
start with the general form of an
equation now what if lets course this is
a point right let suppose this is known
as this this line here is known as the
y-axis right this line is known as the
y-axis and this line over here is known
as the x-axis okay so this line over
here is known as the x-axis and this
point over here with the x-axis and
y-axis meet it's known as the origin now
why it is named as the origin because it
has the point zero and zero the
coordinate of X and the coordinate of Y
is zero in this in this at this point
you can say that so this point can be
say okay this point is Y is 1 and the X
is zero at this line at this at y-axis X
is supposed to be zero at this line on
y-axis
X is zero and on x axis Y is zero so
whichever the point lies on in this
parameter in this parameter so it is
going to give you the coordinates of
that point so if you can see clearly
here a is a point which lies here and it
has coordinates to coordinates x
coordinate and y coordinate which
defines the position of the point ND
claim so what do you get from the X and
y coordinate no it's chase that it is
this much high and this is this shows
it's y coordinate and this gives it x
coordinate so every point let's suppose
R this is y equal to 1 this is y equal
to 2 this is X equal to 1 and the
says X equal to two so let's suppose I
have to draw a point two and two so I'm
going to draw a point of two and two now
always whenever something is given to
you this is the Cartesian product the
Cartesian form of showing the points so
this is the x coordinate and this is the
y coordinate
I hope it's very simple you are able to
understand what I'm trying to explain
here so if I have to draw two two points
so X would be 2 that means X is 2 it
comes here and Y is 2 it comes here so
the point 2 and 2 is going to lie right
here ok so because this is also 2 and
this is also 2 and whenever I write in
this form the x coordinate comes first
and then comes the y coordinate now
let's see now every of what is a line
actually a point is a point a line is a
certain combination of few points so
let's suppose if I draw this line over
here like this now this line contains
all the points over here all the points
constitute this line right so a line
constitutes of many points so if you're
able to understand how a point is formed
you will be able to better understand
how a line is formed now let me show you
let me show you one thing over here now
let's suppose this is a line right and
we have chosen two points at the line so
the first point is that is a x1 y1 and B
x2 y2 right so these are the two points
which lie on the earth on the line so
what do you get from this now let me
just go ahead and calculate the general
form of equation for you before that I
need to show you what slope is what does
the slope measure in a line so if you
just draw back if you just draw back the
line and the clashes with the x axis the
angle that it makes not over here it's
making an angle of alpha with the x axis
the tangent theta of the line of the
angle will give you the slope and it's
usually measured by M
so let's suppose I have this line over
here once I draw it backwards to x-axis
and once I get this angle alpha or beta
or whatever is it and once I calculate
the tangent of that angle this is going
to give me the slope it can be any line
let's suppose the line is like this so
you just draw the line and you calculate
the angle made by by the line and the
x-axis and you calculate the tangent of
the angle and then you're able to
identify these slope so this is the
basic definition of slope I'm not
showing you the methods to calculate
slope though one of the methods is this
method however there are many other
methods with which you can calculate
slope which we'll be doing in further
videos so slope is denoted by M and is
the tangent of the angle which is formed
when you draw the line of to the x-axis
whenever that line clashes with the
x-axis right so this is about slope the
second thing that you require while
forming an equation of a line is the
intercept of the line right so what is
known as the intercept of the line so
intercept of the line I'll show you
let's suppose I again take these two
points right and I gave draw it
backwards now so what is intercept now
intercept is whenever X is equal to zero
the value of y gives you the intercept
and it is denoted by C as you can see
from this line here this this line
clashes or meets the y-axis at this
point so this is going to give me G
intercept right so intercept is the
point whenever X is equal to 0 the value
of intercept will be the value of the y
coordinate so this is going to be this
point is going to be 0 and see always
when indeed whenever the intercept is
there the value of x coordinate will
always be 0 because it is intercept is
always lies on the y axis and let's
suppose the line is this so what I have
to do is I have to draw it backwards
to the XX a y-axis and then I have to
see how
it is how much the how much is the value
of the y-coordinate and that will go is
going to give me the intercept of the
line and this intercept is denoted by
the alphabet C right so now we have done
two things we have done the value R we
have done how what is the slope and we
have defined what is an intercept now
let's see what is the general form of an
equation is so general form of an
equation always is y is equal to MX plus
C right so M over here is going to be
your slope and C over here is going to
be your intercept so all the lines all
the lines are going to satisfy with this
general form of equation and every line
has its unique equation because each
line is going to have unique equations
if two lines have the same equation then
the two lines are similar lines and
every point on that line is going to
satisfy the equation of the line now X
here is any electric pose the line
passes through 2 & 3 right so whenever
you you put this is the value of x
coordinate and this is the value of y
coordinate whenever you put 2 in the
value of x and whenever you put 3 in the
value of y you going this equation is
going to satisfy all all the parts right
so this is the general form of the
equation you do not need to do any more
forms however this is required this is
more than sufficient for preparation for
exams like GMAT sac and GRE and cat so
this is the equation of line that you
must be knowing right this is a this is
very important so every line has its
unique equation and every point on the
line satisfies the equation of the line
fine right let's just do one simple
question we will be doing the complex
questions in the further videos this is
just the basic of the coordinate
geometry so if the equation of the line
is this then what it what is its slope
now we have the equation of line is like
this so let me just rewrite the equation
the equation of the line is 2x plus
3y is equal to 7 now what I have to do
is I just have to bring it to its
general form and from that I can easily
calculate what is the slope or what is
the intercept of the equation now 2x
plus 3y is equal to 7 if I say 3y is
equal to negative of 2x plus 7 so what I
did here I just brought this 2x to this
side and I fur bring the 3 to this side
I can say that Y is equal to minus 2
upon 3x plus 7 by 3 now this is the
general form of the equation where Y is
equal to MX plus C ok now from this you
can easily say that the slope is equal
to negative 2 by 3 and y intercept or
the intercept is equal to 7 by 3 right
so now you can say that that's line
passes through 0 and 7 by 3/5 so this is
one of the point through with line
definitely passes and and this is the
slope of the line right so from just one
equation you can calculate a lot of
things right this was just above the
general form of the equation right what
I want is I want you to go ahead and
watch the further videos where I will be
telling you more about slow more about
the intercepts more about complex
questions fine so this was about this
concept thank you very much and see you
next video
winterkill so we're going ahead to learn
the basic concept of the general
equation of a line this is the first
video for coordinate geometry so my name
is Chris bender Gill and this here is my
email address it's pushpin to 0-8 at
gmail.com don't forget to contact me or
give your valuable feedback and do not
forget to Like us on Facebook the
Facebook link would be on our channel
page right so let's just go ahead and
start with the general form of an
equation now what if lets course this is
a point right let suppose this is known
as this this line here is known as the
y-axis right this line is known as the
y-axis and this line over here is known
as the x-axis okay so this line over
here is known as the x-axis and this
point over here with the x-axis and
y-axis meet it's known as the origin now
why it is named as the origin because it
has the point zero and zero the
coordinate of X and the coordinate of Y
is zero in this in this at this point
you can say that so this point can be
say okay this point is Y is 1 and the X
is zero at this line at this at y-axis X
is supposed to be zero at this line on
y-axis
X is zero and on x axis Y is zero so
whichever the point lies on in this
parameter in this parameter so it is
going to give you the coordinates of
that point so if you can see clearly
here a is a point which lies here and it
has coordinates to coordinates x
coordinate and y coordinate which
defines the position of the point ND
claim so what do you get from the X and
y coordinate no it's chase that it is
this much high and this is this shows
it's y coordinate and this gives it x
coordinate so every point let's suppose
R this is y equal to 1 this is y equal
to 2 this is X equal to 1 and the
says X equal to two so let's suppose I
have to draw a point two and two so I'm
going to draw a point of two and two now
always whenever something is given to
you this is the Cartesian product the
Cartesian form of showing the points so
this is the x coordinate and this is the
y coordinate
I hope it's very simple you are able to
understand what I'm trying to explain
here so if I have to draw two two points
so X would be 2 that means X is 2 it
comes here and Y is 2 it comes here so
the point 2 and 2 is going to lie right
here ok so because this is also 2 and
this is also 2 and whenever I write in
this form the x coordinate comes first
and then comes the y coordinate now
let's see now every of what is a line
actually a point is a point a line is a
certain combination of few points so
let's suppose if I draw this line over
here like this now this line contains
all the points over here all the points
constitute this line right so a line
constitutes of many points so if you're
able to understand how a point is formed
you will be able to better understand
how a line is formed now let me show you
let me show you one thing over here now
let's suppose this is a line right and
we have chosen two points at the line so
the first point is that is a x1 y1 and B
x2 y2 right so these are the two points
which lie on the earth on the line so
what do you get from this now let me
just go ahead and calculate the general
form of equation for you before that I
need to show you what slope is what does
the slope measure in a line so if you
just draw back if you just draw back the
line and the clashes with the x axis the
angle that it makes not over here it's
making an angle of alpha with the x axis
the tangent theta of the line of the
angle will give you the slope and it's
usually measured by M
so let's suppose I have this line over
here once I draw it backwards to x-axis
and once I get this angle alpha or beta
or whatever is it and once I calculate
the tangent of that angle this is going
to give me the slope it can be any line
let's suppose the line is like this so
you just draw the line and you calculate
the angle made by by the line and the
x-axis and you calculate the tangent of
the angle and then you're able to
identify these slope so this is the
basic definition of slope I'm not
showing you the methods to calculate
slope though one of the methods is this
method however there are many other
methods with which you can calculate
slope which we'll be doing in further
videos so slope is denoted by M and is
the tangent of the angle which is formed
when you draw the line of to the x-axis
whenever that line clashes with the
x-axis right so this is about slope the
second thing that you require while
forming an equation of a line is the
intercept of the line right so what is
known as the intercept of the line so
intercept of the line I'll show you
let's suppose I again take these two
points right and I gave draw it
backwards now so what is intercept now
intercept is whenever X is equal to zero
the value of y gives you the intercept
and it is denoted by C as you can see
from this line here this this line
clashes or meets the y-axis at this
point so this is going to give me G
intercept right so intercept is the
point whenever X is equal to 0 the value
of intercept will be the value of the y
coordinate so this is going to be this
point is going to be 0 and see always
when indeed whenever the intercept is
there the value of x coordinate will
always be 0 because it is intercept is
always lies on the y axis and let's
suppose the line is this so what I have
to do is I have to draw it backwards
to the XX a y-axis and then I have to
see how
it is how much the how much is the value
of the y-coordinate and that will go is
going to give me the intercept of the
line and this intercept is denoted by
the alphabet C right so now we have done
two things we have done the value R we
have done how what is the slope and we
have defined what is an intercept now
let's see what is the general form of an
equation is so general form of an
equation always is y is equal to MX plus
C right so M over here is going to be
your slope and C over here is going to
be your intercept so all the lines all
the lines are going to satisfy with this
general form of equation and every line
has its unique equation because each
line is going to have unique equations
if two lines have the same equation then
the two lines are similar lines and
every point on that line is going to
satisfy the equation of the line now X
here is any electric pose the line
passes through 2 & 3 right so whenever
you you put this is the value of x
coordinate and this is the value of y
coordinate whenever you put 2 in the
value of x and whenever you put 3 in the
value of y you going this equation is
going to satisfy all all the parts right
so this is the general form of the
equation you do not need to do any more
forms however this is required this is
more than sufficient for preparation for
exams like GMAT sac and GRE and cat so
this is the equation of line that you
must be knowing right this is a this is
very important so every line has its
unique equation and every point on the
line satisfies the equation of the line
fine right let's just do one simple
question we will be doing the complex
questions in the further videos this is
just the basic of the coordinate
geometry so if the equation of the line
is this then what it what is its slope
now we have the equation of line is like
this so let me just rewrite the equation
the equation of the line is 2x plus
3y is equal to 7 now what I have to do
is I just have to bring it to its
general form and from that I can easily
calculate what is the slope or what is
the intercept of the equation now 2x
plus 3y is equal to 7 if I say 3y is
equal to negative of 2x plus 7 so what I
did here I just brought this 2x to this
side and I fur bring the 3 to this side
I can say that Y is equal to minus 2
upon 3x plus 7 by 3 now this is the
general form of the equation where Y is
equal to MX plus C ok now from this you
can easily say that the slope is equal
to negative 2 by 3 and y intercept or
the intercept is equal to 7 by 3 right
so now you can say that that's line
passes through 0 and 7 by 3/5 so this is
one of the point through with line
definitely passes and and this is the
slope of the line right so from just one
equation you can calculate a lot of
things right this was just above the
general form of the equation right what
I want is I want you to go ahead and
watch the further videos where I will be
telling you more about slow more about
the intercepts more about complex
questions fine so this was about this
concept thank you very much and see you
next video
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