# 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.$$\\ (viii) The coordinates of the point M.$$\\$

From the Figure above,$\\$ (i)The coordinates of point B is the distance of point B from x-axis and y-axis.$\\$ Therefore, the coordinates of point B are $(-5, 2).$$\\ (ii)The coordinates of point C is the distance of point C from x-axis and y-axis.\\ Therefore, the coordinates of point C are (5, -5).$$\\$ (iii)The point that represents the coordinates $(-3, -5)$ is E.$\\$ (iv)The point that represents the coordinates $(2, -4)$ is G.$\\$ (v)The abscissa of point D is the distance of point D from the y-axis. Therefore, the abscissa of point D is $6$.$\\$ (vi)The ordinate of point H is the distance of point H from the x-axis. Therefore, the abscissa of point H is $-3$.$\\$ (vii)The coordinates of point L in the above figure is the distance of point L from x-axis and y-axis. $\\$Therefore, the coordinates of point L are $(0, 5).$$\\ (viii)The coordinates of point M in the above figure is the distance of point M from x-axis and y-axis.\\ Therefore the coordinates of point M are (-3, 0). 5 In which quadrant or on which axis do each of the points (-2, 4), (3, -1), (-1, 0), (1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane. ##### Solution : To determine the quadrant or axis of the points (-2, 4), (3, -1), (-1, 0), (1, 2) and (-3, -5).$$\\$ Plot the plot the points $(-2, 4), (3, -1), (-1, 0), (1, 2)$ and $(-3, -5)$ on the graph, to get $\\$

From the figure above, we can conclude that the points$\\$ $\bullet$ Point $(-2, 4)$ lie in II nd quadrant.$\\$ $\bullet$ Point $(3, -1)$ lie in IV th quadrant.$\\$ $\bullet$ Point $(-1, 0)$ lie on the negative x-axis.$\\$ $\bullet$ Point $(1, 2)$ lie in I st quadrant.$\\$ $\bullet$ Point $(-3, -5)$ lie in III rd quadrant.

6   Plot the points $(x, y)$ given in the following table on the plane, choosing suitable units of distance on the axes.$\\$ $\begin{array}{|c|c|} \hline x& -2 & -1 & 0 & 1 & 3 \\ \hline y & 8 & 7 &-1.25 & 3 & -1 \\ \hline \end{array}$

##### Solution :

Given,$\\$ $\begin{array}{|c|c|} \hline x& -2 & -1 & 0 & 1 & 3 \\ \hline y & 8 & 7 &-1.25 & 3 & -1 \\ \hline \end{array}$

Draw $X'OX$ and $Y'OY$ as the coordinate axes and mark their point of intersection $O$ as the Origin $(0, 0)$$\\ In order to plot the table provided above,\\ \bullet Point A(-2, 8)$$\\$ $\quad \circ$ Take$2$ units on $OX'$ and then $8$ units parallel to $OY$$\\ \bullet Point B (-1, 7)$$\\$ $\quad \circ$ Take $-1$ unit on $OX'$ and then $7$ units parallel to $OY$$\\ \bullet Point C(0, -1.25),\\ \quad \circ Take 1.25 units below x-axis on OY' on the y-axis\\ \bullet Point D(1, 3)$$\\$ $\quad \circ$ Take $1$ unit on $OX$ and then $3$ units parallel to $OY$$\\ \bullet Point E(3, -1),$$\\$ $\quad \circ$Take $3$ units on $OX$ and then move $1$ unit parallel to $OY'$