## 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

1. Plotting the points on the graph paper.
2. Cartesian system.
3. 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

1. Draw any figure on the graph paper in first quadrant (say, a figure of stairs).
2. 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.
3. join A, B, C, D, E, F, G as shown infig. (i).
4. Consider y-axis as a mirror.
5. 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).
6. Join A’, B’, C’, D’, E’, F’, G’ we get the image of the stairs.
7. Note down the coordinates of image so formed and record them in observation Table 1.
8. 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.
9. Now, we will get image in fourth quadrant.
10. 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

1. 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.
2. 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

1. The same activity can be performed for other figures like quadrilaterals, triangles, stars or any polygon.
2. 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 ?
A cartesian system consists of x-axis and y-axis in a plane.

Question 2.
What is ordinate ?
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.
(-1,3).

Question 4.
What is the image of the (-1, -5) in IV quadrant ?
(1,-5).

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

Question 6.
Give one point which lies on x-axis ?
(3,0) or (-5,0).

Question 7.
Give one point which lies on y-axis ?
(0,7) or (0,-8)

Question 8.
Whatis the main use of cartesian system?
To locate the position of a point in the plane.

Question 9.
What type of graph do you get for x = 2 ?
A straight line parallel to y-axis at the distance of 2 unit from origin.

Question 10.
Write x = -5 in two variable form.
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 ?
(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