Answer

Verified

391.6k+ views

Hint: The \[x\] coordinate of a point determines its distance from the \[y\] axis and the \[y\] coordinate of the point determines its distance from the \[x\] axis . A line parallel to the $x$ axis is of the form $y=c$ and a line parallel to the $y$ axis is of the form $x=c$ , where $c$ is any constant.

Complete step-by-step answer:

Before plotting the points , we must know about the coordinate system.

The cartesian coordinate system is a system of identifying the location of a point with respect to two perpendicular lines , known as coordinate axes. The vertical axis is called the \[y\] axis and the horizontal axis is called the \[x\] axis. The point of intersection of these axes is called the origin and it is represented by the ordered pair \[(0,0)\]. The distance of a point from the \[y\] axis is called the \[x\]coordinate and the distance of the point from \[x\] axis is called the \[y\] coordinate of the point. The equation of a line passing through a point $\left( {{x}_{1}},{{y}_{1}} \right)$ is given as $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$ , where $m$ is the slope of the line. Now, if the line is parallel to the $x$ axis, then its slope is equal to zero . So, the equation of the line will be $y-{{y}_{1}}=0$ . So, the $y$ coordinate of any point on the line will be ${{y}_{1}}$. Similarly, if the line is parallel to the $y$ axis, then the slope of the line will be equal to infinity, and the equation of the line will be of the form $x-{{x}_{1}}=0$ . So, the $x$ coordinate of any point on the line will be ${{x}_{1}}$.

Now, coming to the question, the pair of equations given to us are $x=a$ and $y=b$. The equation $x=a$ is of the form $x-{{x}_{1}}=0$ , and hence, represents a line parallel to $y$ axis at a distance of $a$ units from it. Similarly, the equation $y=b$ is of the form $y-{{y}_{1}}=0$ , and hence, represents a line parallel to the $x$ axis at a distance of $b$ units from it. Hence, the two lines are perpendicular and therefore, will intersect at a point. Now, any point on the line $x=a$ will have its $x$ coordinate equal to $a$ and any point on the line $y=b$ will have its $y$ coordinate equal to $b$ . So, the coordinates of the point of intersection of the lines $x=a$ and $y=b$ will be $\left( a,b \right)$ .

This can be represented graphically as:

So, the lines $x=a$ and $y=b$ are intersecting lines and they intersect at the point $\left( a,b \right)$.

Hence, option D. is the correct option.

Note: Students get confused and write that the line $x=a$ is parallel to the $x$ axis , which is wrong. Such confusion should be avoided.

Complete step-by-step answer:

Before plotting the points , we must know about the coordinate system.

The cartesian coordinate system is a system of identifying the location of a point with respect to two perpendicular lines , known as coordinate axes. The vertical axis is called the \[y\] axis and the horizontal axis is called the \[x\] axis. The point of intersection of these axes is called the origin and it is represented by the ordered pair \[(0,0)\]. The distance of a point from the \[y\] axis is called the \[x\]coordinate and the distance of the point from \[x\] axis is called the \[y\] coordinate of the point. The equation of a line passing through a point $\left( {{x}_{1}},{{y}_{1}} \right)$ is given as $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$ , where $m$ is the slope of the line. Now, if the line is parallel to the $x$ axis, then its slope is equal to zero . So, the equation of the line will be $y-{{y}_{1}}=0$ . So, the $y$ coordinate of any point on the line will be ${{y}_{1}}$. Similarly, if the line is parallel to the $y$ axis, then the slope of the line will be equal to infinity, and the equation of the line will be of the form $x-{{x}_{1}}=0$ . So, the $x$ coordinate of any point on the line will be ${{x}_{1}}$.

Now, coming to the question, the pair of equations given to us are $x=a$ and $y=b$. The equation $x=a$ is of the form $x-{{x}_{1}}=0$ , and hence, represents a line parallel to $y$ axis at a distance of $a$ units from it. Similarly, the equation $y=b$ is of the form $y-{{y}_{1}}=0$ , and hence, represents a line parallel to the $x$ axis at a distance of $b$ units from it. Hence, the two lines are perpendicular and therefore, will intersect at a point. Now, any point on the line $x=a$ will have its $x$ coordinate equal to $a$ and any point on the line $y=b$ will have its $y$ coordinate equal to $b$ . So, the coordinates of the point of intersection of the lines $x=a$ and $y=b$ will be $\left( a,b \right)$ .

This can be represented graphically as:

So, the lines $x=a$ and $y=b$ are intersecting lines and they intersect at the point $\left( a,b \right)$.

Hence, option D. is the correct option.

Note: Students get confused and write that the line $x=a$ is parallel to the $x$ axis , which is wrong. Such confusion should be avoided.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

What percentage of the solar systems mass is found class 8 physics CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you graph the function fx 4x class 9 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE