**CBSE Class 9 Maths Lab Manual – Coordinate Geometry**

**Objective**

To obtain the mirror image of a given geometrical figure with respect to x-axis and y-axis.

**Prerequisite Knowledge**

- Plotting the points on the graph paper.
- Cartesian system.
- The perpendicular distance between the mirror and the image of point P is equal to the perpendicular distance between the point P and the mirror.

**Materials Required**

Graph paper, pencil (coloured), eraser, ruler and mirror.

**Procedure**

- Draw any figure on the graph paper in first quadrant (say, a figure of stairs).
- For stairs, plot some points say, A(3,0), B(3,1), C(2,1), D(2,2), E(1,2), F(1,3), G(0,3) with coloured pencils.
- join A, B, C, D, E, F, G as shown infig. (i).
- Consider y-axis as a mirror.
- Fold the graph along the y-axis to get the images of points A, B, C, D, E, F, G in second quadrant as A’, B’, C’, D’, E’, F’, G’ respectively as shown in fig. (i).
- Join A’, B’, C’, D’, E’, F’, G’ we get the image of the stairs.
- Note down the coordinates of image so formed and record them in observation Table 1.
- Repeat the procedure for the same stairs with respect to x-axis i.e, to get image of the stairs taking x-axis as mirror.
- Now, we will get image in fourth quadrant.
- Note down the coordinates of image along x-axis and record in Table 2.

**Mirror image w.r.t. y-axis**

**Mirror image w.r.t. x-axis**

**Observation and Calculation**

**Table 1 (Image along y-axis)**

S.No. | Coordinates of Fig.ABCDEFG | Coordinates of image A’ B’ C’ D’ E’ F’ G’ |

1. | A (3,0) | A’ (-3,0) |

2. | B (3,1) | B’ (-3,1) |

3. | C (2,1) | C’ (-2,1) |

4. | D (2,2) | D’ (-2,2) |

5. | E (1,2) | E’ (-1,2) |

6. | F (1,3) | F’ (-1,3) |

7. | G (0,3) | G’ (0,3) |

**Table 2 (Image along x-axis)**

S.No. | Coordinates of Fig.ABCDEFG | Coordinates of image A’ B’ C’ D’ E’ F’ G’ |

1. | A (3,0) | A’ (3,0) |

2. | B (3,1) | B’ (3, -1) |

3. | C (2,1) | C’ (2, -1) |

4. | D (2,2) | D’ (2, -2) |

5. | E (1,2) | E’ (1, -2) |

6. | F (1,3) | F’ (1, -3) |

7. | G (0,3) | G’ (0, -3) |

**Result**

We have obtained the mirror images of figures along x-axis and y-axis.

**Learning Outcome**

**Mirror image with respect to x-axis:**In this case, image of P (x,y) become P (x, -y). Thus, to find the image of any point along the x-axis, we keep the x-coordinate same and sign of y-coordinate gets changed. Any point on the mirror remains the same.**Mirror image with respect to y-axis:**In this case, image of P (x,y) becomes P (-x,y). Thus, to find the image of any point with respect to y-axis, we keep the y-coordinate same and sign of x-coordinate gets changed.

**Activity Time**

- The same activity can be performed for other figures like quadrilaterals, triangles, stars or any polygon.
- Draw the mirror image of the figure shown, in the second quadrant by plotting different corner points of figure.

**Viva Voce**

**Question 1.**

What is cartesian system ?

**Answer:**

A cartesian system consists of x-axis and y-axis in a plane.

**Question 2.**

What is ordinate ?

**Answer:**

Distance of a point in a plane from the x-axis is known as ordinate.

**Question 3.**

(1,3) lies in first quadrant, what is the image of this point in II quadrant.

**Answer:**

(-1,3).

**Question 4.**

What is the image of the (-1, -5) in IV quadrant ?

**Answer:**

(1,-5).

**Question 5.**

What is the image of (3, -5) is I quadrant ?

**Answer:**

(3,5)

**Question 6.**

Give one point which lies on x-axis ?

**Answer:**

(3,0) or (-5,0).

**Question 7.**

Give one point which lies on y-axis ?

**Answer:**

(0,7) or (0,-8)

**Question 8.**

Whatis the main use of cartesian system?

**Answer:**

To locate the position of a point in the plane.

**Question 9.**

What type of graph do you get for x = 2 ?

**Answer:**

A straight line parallel to y-axis at the distance of 2 unit from origin.

**Question 10.**

Write x = -5 in two variable form.

**Answer:**

0.y + 1.x = -5.

**Multiple Choice Questions**

**Question 1.**

Mention the quadrant in which (1,-1) lie:

(i) II

(ii) III

(iii) IV

(iv) none of these

**Question 2.**

Which of the given coordinates A(-1,0), B(0,2) lie on x-axis ?

(i) A(-1,0)

(ii) B(0,2)

(iii) neither A nor B

(iv) both A and B

**Question 3.**

Which of the given coordinates C(3,0), D(0, -5) lie on y-axis ?

(i) D(0-5)

(ii) C(3,0)

(iii) both D and C

(iv) neither C nor D

**Question 4.**

The origin (0,0) lie on which axis ?

(i) y-axis

(ii) x-axis

(iii) both axis

(iv) neither x-axis nor y-axis

**Question 5.**

Which of the points A(5, 4), B(-5, 0), C(0, -4), D(5, -3) do not lie in any quadrant ?

(i) B(-5,0)

(ii) B and C

(iii) C and D

(iv) none of these

**Question 6.**

Write the coordinates of a point lying onj/-axis at a distance of 5 units.

(i) (0,5)

(ii) (5,0)

(iii) (5,5)

(iv) none of these

**Question 7.**

Write the coordinates of a point lying on x-axis to the left of origin at a distance of 2 units.

(i) (2,-2)

(ii) (0,2)

(iii) (-2,0)

(iv) none of these

**Question 8.**

In which quadrant will the point lie, if the ordinate is 3 and abscissa is-4?

(i) II

(ii)III

(iii) IV

(iv) I

**Question 9.**

What is the name of each part of the plane formed by x’-axis andj-axis ?

(i) Quadrant

(ii) octant

(iii) x-y plane

(iv) none of these

**Question 10.**

Write the abscissa and ordinate of (-3,4) :

(i) abscissa = 4, ordinate = -3

(ii) abscissa = -3, ordinate = 4

(iii) abscissa = 7, ordinate = 1

(iv) none of these

**Answers**

- (iii)
- (i)
- (i)
- (iii)
- (ii)
- (i)
- (iii)
- (i)
- (i)
- (ii)

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