Math Labs with Activity – Obtain the Mirror Image of a Given Geometrical Figure
To obtain the mirror image of a given geometrical figure with respect to the r-axis and the y-axis.
- A few graph papers
- A pencil
- A ruler
The perpendicular distance between the mirror and the image P’ of a point P is equal to the perpendicular distance.
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).
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).
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.
- 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.
Remarks: The teacher must assist the students to work out the same activity for other figures such as quadrilaterals and polygons.