Examples (Revised) - Chapter 3 - Coordinate Geometry - Ncert Solutions class 9 - Maths

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Chapter 3: Coordinate Geometry - NCERT Solutions for Class 9 Maths

Example 1 :

See Fig.and complete the following statements:
(i) The abscissa and the ordinate of the point $\mathrm{B}$ are ______ and ___________, respectively. Hence, the coordinates of $\mathrm{B}$ are $\qquad$ _, _).
(ii) The $x$-coordinate and the $y$-coordinate of the point $\mathrm{M}$ are __________ and _____________ , respectively. Hence, the coordinates of $\mathrm{M}$ are ( _, _ _).
(iii) The $x$-coordinate and the $y$-coordinate of the point $\mathrm{L}$ are ____________ and ____________ , respectively. Hence, the coordinates of $\mathrm{L}$ are ( _, _ _).
(iv) The $x$-coordinate and the $y$-coordinate of the point $\mathrm{S}$ are ___________ and __________ , respectively. Hence, the coordinates of $\mathrm{S}$ are ( _, _ _).

Solution:

(i) Since the distance of the point B from the $y$-axis is 4 units, the $x$ - coordinate or abscissa of the point $\mathrm{B}$ is 4 . The distance of the point $\mathrm{B}$ from the $x$ - axis is 3 units; therefore, the $y$-coordinate, i.e., the ordinate, of the point $\mathrm{B}$ is 3 . Hence, the coordinates of the point $\mathrm{B}$ are $(4,3)$.
As in (i) above :
(ii) The $x$-coordinate and the $y$-coordinate of the point $\mathrm{M}$ are -3 and 4 , respectively. Hence, the coordinates of the point $\mathrm{M}$ are $(-3,4)$.
(iii) The $x$-coordinate and the $y$-coordinate of the point $\mathrm{L}$ are -5 and -4 , respectively. Hence, the coordinates of the point $\mathrm{L}$ are $(-5,-4)$.
(iv) The $x$-coordinate and the $y$-coordinate of the point $\mathrm{S}$ are 3 and -4 , respectively. Hence, the coordinates of the point $\mathrm{S}$ are $(3,-4)$.

Example 2 :

Write the coordinates of the points marked on the axes in Fig.

Solution :

You can see that :
(i) The point $\mathrm{A}$ is at a distance of +4 units from the $y$-axis and at a distance zero from the $x$-axis. Therefore, the $x$ - coordinate of A is 4 and the $y$ - coordinate is 0 . Hence, the coordinates of $\mathrm{A}$ are $(4,0)$.
(ii) The coordinates of $\mathrm{B}$ are $(0,3)$. Why?
(iii) The coordinates of $\mathrm{C}$ are $(-5,0)$. Why?
(iv) The coordinates of $\mathrm{D}$ are $(0,-4)$. Why?
(v) The coordinates of $\mathrm{E}$ are $\left(\frac{2}{3}, 0\right)$. Why?

Since every point on the $x$ - axis has no distance (zero distance) from the $x$ - axis, therefore, the $y$-coordinate of every point lying on the $x$-axis is always zero. Thus, the coordinates of any point on the $x$ - axis are of the form $(x, 0)$, where $x$ is the distance of the point from the $y$-axis. Similarly, the coordinates of any point on the $y$ - axis are of the form $(0, y)$, where $y$ is the distance of the point from the $x$-axis. Why?

What are the coordinates of the origin $\mathbf{O}$ ? It has zero distance from both the axes so that its abscissa and ordinate are both zero. Therefore, the coordinates of the origin are $\mathbf{( 0 , 0 )}$.

In the examples above, you may have observed the following relationship between the signs of the coordinates of a point and the quadrant of a point in which it lies.
(i) If a point is in the 1 st quadrant, then the point will be in the form $(+,+)$, since the 1st quadrant is enclosed by the positive $x$ - axis and the positive $y$ - axis.
(ii) If a point is in the 2 nd quadrant, then the point will be in the form $(-,+)$, since the 2nd quadrant is enclosed by the negative $x$ - axis and the positive $y$-axis.
(iii) If a point is in the 3rd quadrant, then the point will be in the form $(-,-)$, since the 3rd quadrant is enclosed by the negative $x$ - axis and the negative $y$-axis.
(iv) If a point is in the 4th quadrant, then the point will be in the form $(+,-)$, since the 4th quadrant is enclosed by the positive $x$ - axis and the negative $y$ - axis (see Fig. 3.13).