Question

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

Answer 1

Step 1: Draw the desired figure (say a triangle A1B1C1) on the graph paper by plotting the coordinates of its vertices A1, B1, and C1 and then joining them (see Figure 31.1).

Math Labs with Activity - Obtain the Mirror Image of a Given Geometrical Figure 1

Step 2: Drop perpendiculars A1L1, B1M1 and C1N1 on the x-axis and extend these lines to the points A1‘, B1‘ and C1‘ respectively so that A1L1 = L1A1‘, B1M1 =M1B1‘ and C1N1 = N1C1‘

Step 3: Join A1‘B1‘C1‘ to get the mirror image of the triangle A1B1C1 (as shown in Figure 31.1) with respect to the x-axis.

Step 4: Find the coordinates of A1‘, B1‘ and C1‘. Record them in Observation Table 1.

Step 5: Draw any other triangle A2B2C2 on the graph paper by plotting the coordinates of its vertices A2, B2 and C2 and then joining them (see Figure 31.2).

Math Labs with Activity - Obtain the Mirror Image of a Given Geometrical Figure 2

Step 6: Drop perpendiculars A2L2, B2M2 and C2N2 on the y-axis and extend these lines to the points A2‘, B2‘ and C2‘ respectively so that A2L2 =L2A2‘, B2M2 =M2B2‘ and C2N2 =N2C2‘.

Step 7: Join A2‘B2‘C2‘ to obtain the mirror image of the triangle A2B2C2 (as shown in Figure 33.2) with respect to the y-axis.

Step 8: Find the coordinates of A2‘, B2‘ and C2‘. Record them in Observation Table 2.

Step 9: Similarly, draw other figures on the graph paper and obtain their mirror images with respect to the x-axis and y-axis. Record the observations (the coordinates of the vertices of the figure along with those of the mirror image) in the two observation tables.

Observations

Math Labs with Activity - Obtain the Mirror Image of a Given Geometrical Figure 3

Math Labs with Activity - Obtain the Mirror Image of a Given Geometrical Figure 4

Results

Mirror image with respect to x-axis The mirror image of a point P(x, y) with respect to x-axis is the point P'(x, -y). Thus, to find the image of a point in the x-axis, we keep the x-coordinate same and change the sign of the y-coordinate.

Mirror image with respect to y-axis The mirror image of a point P(x, y) with respect to y-axis is the point P'(-x, y). Thus, to find the image of a point in the y-axis, we change the sign of the x-coordinate and keep the y-coordinate same.