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

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

1. A few graph papers
2. A pencil
3. 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 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.

Observations

Results

1. 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.
2. 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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