Lab Manual: Coordinate Geometry | Lab Manuals for Class 9 PDF Download

Objective

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)

Table 2 (Image along x-axis)

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.