Question

What are the name horizontal and vertical lines drawn to determine the position at any point in the cartesian plane?

Answer 1

Hint: We should know about the co-ordinate geometry in the cartesian plane has two axes, one is the x-axis and the second one is the y-axis which is represented as a point $P(x,y)$. And two are perpendicular to each other means the angle between the two axes is 90 degrees.

Complete step-by-step solution:
Let us draw the cartesian plane to explain all the terms clearly.

The given question can be explained in the following points.
1)The name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane is the x-axis and y-axis respectively.
Here the horizontal line is always x-axis and the vertical line is always y-axis and these lines are always perpendicular to each other.
For example, let us consider a point $P\left( 2,3 \right)$ here the “2” belongs to the x-axis and “3” belongs to
the y-axis.
2)The name of each part of the plane formed by these two lines x-axis and the y-axis is quadrants and
these quadrants classified into four types.
a) First Quadrant,
b) Second Quadrant,
c) Third Quadrant,
d) the Fourth Quadrant.
In first quadrant only both x-axis and y-axis are positive that is \[\left( +,+ \right)\].
In second quadrant x-axis is negative and y-axis is positive that is \[\left( -,+ \right)\].
In third quadrant x-axis is negative and y-axis is also negative that is \[\left( -,- \right)\].
In fourth quadrant x-axis is positive and y-axis is negative that is \[\left( +,- \right)\].
3)The point where these two lines intersect is called “Origin” that is represented as $\left( 0,0 \right)$ means
$x=0$ and $y=0$ which is generally represented with a letter called “O”.

Note: We should always remember that the x-axis and y-axis are perpendicular to each other and are represented as x-axis and y-axis. We should know that in the point $\left( x,y \right)$ x is known as x-coordinate or abscissa and y is known as y-coordinate or ordinate. The points are formed by the intersection of two lines in which one is parallel to the x-axis and the other is parallel to the y-axis. We should know that the slope of a horizontal line (x-axis) is 0 and the vertical line (y-axis) is undefined.