Coordinate Geometry

Class 9 NCERT Maths

NCERT

1   How will you describe the position of a table lamp on your study table to another person?

Solution :

Let us consider the given below figure of a study stable, on which a study lamp is placed.$\\$ From the Figure Above,$\\$ $\bullet$ Consider the lamp on the table as a point$\\$ $\bullet$ Consider the table as a plane.$\\$ $\bullet$ We can conclude that the table is rectangular in shape, when observed from the top.$\\$ $\ \ \ \ \ \ \ \ \ \circ$The table has a short edge and a long edge$\\$ $\ \ \ \ \ \ \ \ \ \circ$Let us measure the distance of the lamp from the shorter edge and the longer edge.$\\$ $\ \ \ \ \ \ \ \ \ \circ$Let us assume$\\$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \diamond$ Distance of the lamp from the shorter edge is $15 cm$$\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \diamond Distance of the lamp from the longer edge, its 25 cm.$$\\$ Therefore, we can conclude that the position of the lamp on the table can be described in two ways depending on the order of the axes as $(15, 25)$ or $(25, 15).$

2   (Street Plan): A city has two main roads which cross each other at the center of the city. These two roads are along the North–South direction and East-West direction. All the other streets of the city run parallel to these roads and are $200 m$ apart. There are $5$ streets in each direction. Using $1 cm = 200 m,$ draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross- street is made by two streets, one running in the North-South direction and another in the East- West direction. Each cross street is referred to in the following manner: If the $2^{ nd}$ street running in the North-South direction and $5^{ th}$ in the East-West direction meet at some crossing, then we will call this cross-street $(2, 5)$. Using this convention, find:$\\$ (i) How many cross - streets can be referred to as $(4, 3).$$\\ (ii) How many cross - streets can be referred to as (3, 4).$$\\$

Solution :

$\bullet$ Draw two perpendicular lines as the two main roads of the city that cross each other at the center$\\$ $\bullet$ Mark it as N-S and E-W.$\\$ $\bullet$ Let us take the scale as $1 cm = 200 m.$$\\ \bullet Draw five streets that are parallel to both the main roads, to get the given below figure.\\ Street plan is as shown in the figure:\\ (i) There is only one cross street, which can be referred as (4, 3).\\ (ii) There is only one cross street, which can be referred as (3, 4).$$\\$

3   Write the answer of each of the following questions:$\\$ (i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?$\\$ (ii) What is the name of each part of the plane formed by these two lines?$\\$ (iii) Write the name of the point where these two lines intersect.

Solution :

(i) The horizontal line that is drawn to determine the position of any point in the Cartesian plane is called as x-axis.$\\$ The vertical line that is drawn to determine the position of any point in the Cartesian plane is called as y-axis.$\\$ (ii) The name of each part of the plane that is formed by x-axis and y-axis is called as quadrant.$\\$ (iii) The point, where the x-axis and the y-axis intersect is called as origin (O)$\\$

4   See the figure, and write the following:$\\$ (i) The coordinates of $B.$$\\ (ii) The coordinates of C.$$\\$ (iii) The point identified by the coordinates $(-3, -5).$$\\ (iv) The point identified by the coordinates (2, -4).$$\\$ (v) The abscissa of the point $D.$$\\ (vi) The ordinate of the point H.$$\\$ (vii) The coordinates of the point $L.$$\\ (viii) The coordinates of the point M.$$\\$