Question

What is the $x-$coordinate of the ordered pair $\left( 4,13 \right)?$

Answer 1

We know that we denote every point in the $xy-$ plane which we call a coordinate plane also with an ordered pair, as we know, consists of two numbers either positive or negative or zero. We write the $x-$coordinate as the first in the ordered pair.

Complete step-by-step answer:
Let us consider the given ordered pair, $\left( 4,13 \right).$
We are asked to find the $x-$coordinate in this ordered pair.
Now, let us consider the $xy-$plane which we often call the coordinate plane. We represent the points that are called the coordinate points with ordered pairs of numbers.
Let us consider a point in the $xy-$plane.
Now, let us suppose that this point lies in the plane at a place where the corresponding value in the $x-$axis is $x$ and the corresponding value in the $y-$axis is $y.$ Then, we represent this point with the ordered pair $\left( x,y \right).$ So, we can say that the $x-$coordinate of the point or the ordered pair is $x$ and the $y-$coordinate of the point or the ordered pair is $y.$
So, it is clear that, when we deal with the ordered pair, we write the $x-$coordinate as the first element and then the $y-$coordinate as the second element.
So, we can say that the first element in the given ordered pair $\left( 4,13 \right)$ is the first element.
And as we can see, $4$ is the first element in the given ordered pair.
Hence, the $x-$coordinate of the given ordered pair is $4.$

Note: If we are asked to find the $y-$coordinate, then we should go with the second element which in this case is $13.$ If we are dealing with a coordinate system where there are three coordinate axes, we usually represent them as $x,y$ and $z$ axes and the coordinate point will be a triplet containing three points as $\left( x,y,z \right).$