On the basis of chapter straight lines prove that X&Y axis of cartesian plane are perpendicular to each other.

Answer 1

I'm not sure what you mean by basis of chapter straight lines.

Here's how i would prove it.
I would first draw a a set of points including (-2,2) (0,2) (2,2) (4,2).
then I would connect those poitns to form a line, and find the slope of the line. Considering that the slope is y/x, the slope of any two given points on that line would be 0/2 or 0.
We just proved that this is a horizontal line at y=2 with a slope of zero.

Next, draw points on (-2,0) (0,0) (2,0) (4,0), along the x axis, and connect those poitns. this is a line at y=0 (the x axis). finding the slope again shows that it is horizontal. (m=0).

These two lines are parallel.

Now draw your vertical lines.
First, draw a line along the points (2, -2) (2, 0) (2,2) (2,4)
connect these points to draw a line at x=2, find the slope
your slope should be 2/0, which is undefined, thus proving that it's a horizontal line.

Now draw a line along the y-axis using points (0, -2) (0, 0) (0,2) (0,4). This line a x=0 is parallel to the line at x=2, but we can't prove that they have the same slope because they're both undefined.

Now, because the lines x=2 and y=2 have slopes that are the negative reciprocal of eachother (0/2 = -2/0[undefined]), those are perpendicular. and because x=2 and x=0 are parallel, and y=2 and y=0 are parallel, lines x=0 and y=0 are perpendicular.
Thus, the x and y axis are perpendicular.

Answer 2

The definition of a Cartesian plane neccesitates that the X an Y axis are perpendicular

Answer 3

in the chapter straight lines the is a formula concerning the slope of 2 lines;tan(anglebetwn 2 lines)=M-m/1+M*m.the two axes have their eqns as x=0 and y=0.let M be the slope of x axis and m the slope of y axis.if the equation of a line that has both components be
ax+by+c=0we know that the product of slopes is given by
de=c/a and sum of slopes is given by d+e =-b/a,where d,e are the roots of the above eqn.in the case M AND m DO HAPPEN TO SATISFY THE ABOVE EQN,then M*m=-1.;c a are of opposite signs in the above equation.hence tan(angle)=infinity,and by definition angle =90.hence the x and y axes of the cartesian plane are perpendicular to each other.

Answer 4

Cartesian Plane information

Click on the URL below for additional information concerning Cartesian Plans

en.wikipedia.org/wiki/Cartesian_coordinate_system

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Answer 5

actual. remedy for y and also you could get 3/2. For the 2d bit, you comprehend that y can not impact the fee of the curve, so that you comprehend that y must be more suitable with techniques from 0. social gathering 0*y = x+a million you should have a time period that does isn't more suitable with techniques from x, or you receives a line that runs on properly of the y axis.

Answer 6

Who says they need to be perpendicular to each other..
x and y axis can be inclined at an angle to each other ..
x and y axis r taken to be perpendicular so as the x component in y direction is 0.

Answer 7

Origin, and the X and Y axes are predefined in Cartesian plane.