## I**mportant Questions & Solutions for Class 9 Chapter 3 (Coordinate Geometry)**

**1. Write the coordinates of each of the points P, Q, R, S, T and O from the figure given.**

Solution:

The coordinates of the points P, Q, R, S, T and O are as follows:

P = (1, 1)

Q = (-3, 0)

R = (-2, -3)

S = (2, 1)

T = (4, -2)

O = (0, 0)

**Q.2: Plot the following points and check whether they are collinear or not:**

**(i) (1, 3), (â€“ 1, â€“ 1), (â€“ 2, â€“ 3)**

**(ii) (1, 1), (2, â€“ 3), (â€“ 1, â€“ 2)**

**(iii) (0, 0), (2, 2), (5, 5)**

Solution:

(i)

The points (1, 3), (â€“ 1, â€“ 1), (â€“ 2, â€“ 3) lie in a straight line,

Hence, the points are collinear.

(ii)

The points (1, 1), (2, â€“ 3), (â€“ 1, â€“ 2) do not lie in a straight line,

Hence, the points are not collinear.

(iii)

The points (0, 0), (2, 2), (5, 5) lie in a straight line,

Hence, the points are collinear.

**Q.3: Without plotting the points indicate the quadrant in which they will lie, if**

**(i) ordinate is 5 and abscissa is â€“ 3**

**(ii) abscissa is â€“ 5 and ordinate is â€“ 3**

**(iii) abscissa is â€“ 5 and ordinate is 3**

**(iv) ordinate is 5 and abscissa is 3**

Solution:

(i) The point is (-3,5).

Hence, the point lies in the II quadrant.

(ii) The point is (-5,-3).

Hence, the point lies in the III quadrant.

(iii) The point is (-5,3).

Hence, the point lies in the II quadrant.

(iv) The point is (3,5).

Hence, the point lies in the I quadrant.

**Q.4: See figure and write the following:**

**The coordinates of B.****The coordinates of C.****The point identified by the coordinates (â€“3, â€“5).****The point identified by the coordinates (2, â€“ 4).****The abscissa of the point D.****The ordinate of the point H.****The coordinates of the point L.****The coordinates of the point M.**

Solution:

- The co-ordinates of B is (âˆ’5, 2).
- The co-ordinates of C is (5, âˆ’5).
- The point identified by the coordinates (âˆ’3, âˆ’5) is E.
- The point identified by the coordinates (2, âˆ’4) is G.
- Abscissa means x co-ordinate of point D. So, abscissa of the point D is 6.
- Ordinate means y coordinate of point H. So, the ordinate of point H is -3.
- The coordinates of the point L is (0, 5).
- The coordinates of the point M is (âˆ’3, 0).

**Q.5: Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.**

x |
-2 |
-1 |
0 |
1 |
3 |

y |
8 |
7 |
-1.25 |
3 |
-1 |

Solution:

The points to plotted on the(x,y) are:

- (-2,8)
- (-1,7)
- (0,-1.25)
- (1,3)
- (3,-1)

On the graph mark X-axis and Y-axis. Mark the meeting point as O.

Now, Let 1 unit = 1 cm

- (-2,8): II- Quadrant, Meeting point of the imaginary lines that starts from 2 units to the left of origin O and from 8 units above the origin O
- (-1,7): II- Quadrant, Meeting point of the imaginary lines that starts from 1 units to the left of origin O and from 7 units above the origin O
- (0,-1.25): On the y-axis, 1.25 units to the bottom of origin O
- (1,3): I- Quadrant, Meeting point of the imaginary lines that starts from 1 units to the right of origin O and from 3 units above the origin O
- (3,-1): IV- Quadrant, Meeting point of the imaginary lines that starts from 3 units to the right of origin O and from 1 unit below the origin O

**Q.6: Write the answer to each of the following questions:**

**(i) What is the name of the 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 name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane is x-axis and y-axis respectively.

(ii) The name of each part of the plane formed by these two lines x-axis and the y-axis is quadrants.

(iii) The point where these two lines intersect is called the origin

### Extra Questions For Class 9th Maths Chapter 3

- Points A (5, 3), B (â€“2, 3) and D (5, â€“4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.
- Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the third quadrant.
- Plot the points (x, y) given by the following table:

x | 2 | 4 | -3 | -2 |

y | 4 | 2 | 0 | 5 |

4. Plot the following points and write the name of the figure obtained by joining them in order:

P(â€“ 3, 2), Q (â€“ 7, â€“ 3), R (6, â€“ 3), S (2, 2)

5. Locate the points (5, 0), (0, 5), (2, 5), (5, 2), (â€“3, 5), (â€“3, â€“5), (5, â€“3) and (6, 1) in the Cartesian plane.