**Math Labs with Activity – Obtain the Mirror Image of a Given Geometrical Figure**

**OBJECTIVE**

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

**Materials Required**

- A few graph papers
- A pencil
- A ruler

**Theory**

The perpendicular distance between the mirror and the image P’ of a point P is equal to the perpendicular distance.

**Procedure**

**Step 1:** Draw the desired figure (say a triangle A_{1}B_{1}C_{1}) on the graph paper by plotting the coordinates of its vertices A_{1}, B_{1}, and C_{1} and then joining them (see Figure 31.1).

**Step 2:** Drop perpendiculars A_{1}L_{1}, B_{1}M_{1} and C_{1}N_{1} on the x-axis and extend these lines to the points A_{1}‘, B_{1}‘ and C_{1}‘ respectively so that A_{1}L_{1} = L_{1}A_{1}‘, B_{1}M_{1} =M_{1}B_{1}‘_{ }and C_{1}N_{1} = N_{1}C_{1}‘

**Step 3:** Join A_{1}‘B_{1}‘C_{1}‘ to get the mirror image of the triangle A_{1}B_{1}C_{1} (as shown in Figure 31.1) with respect to the x-axis.

**Step 4:** Find the coordinates of A_{1}‘, B_{1}‘ and C_{1}‘. Record them in Observation Table 1.

**Step 5:** Draw any other triangle A_{2}B_{2}C_{2} on the graph paper by plotting the coordinates of its vertices A_{2}, B_{2} and C_{2} and then joining them (see Figure 31.2).

**Step 6:** Drop perpendiculars A_{2}L_{2}, B_{2}M_{2} and C_{2}N_{2} on the y-axis and extend these lines to the points A_{2}‘, B_{2}‘_{ }and C_{2}‘ respectively so that A_{2}L_{2} =L_{2}A_{2}‘, B_{2}M2 =M_{2}B_{2}‘ and C_{2}N_{2} =N_{2}C_{2}‘.

**Step 7:** Join A_{2}‘B_{2}‘C_{2}‘ to obtain the mirror image of the triangle A_{2}B_{2}C_{2} (as shown in Figure 33.2) with respect to the y-axis.

**Step 8:** Find the coordinates of A_{2}‘, B_{2}‘ and C_{2}‘. 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**

**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.

**Remarks:** The teacher must assist the students to work out the same activity for other figures such as quadrilaterals and polygons.

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