A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares, upto 5 more may be coloured black. Which one among the following options depicts the minimum number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is representative)
To achieve two lines of symmetry in the given figure with a minimum number of additional black squares, we need to strategically select which squares should be colored black.
The existing black squares provide partial symmetry, and we can utilize this by adding black squares to mirror these along potential lines of symmetry.
The lines of symmetry can be vertical and horizontal through the center of the figure.
Currently, the squares a and b, e and h, and j and k are symmetrically opposite. This indicates the need to focus on the center squares for achieving symmetry.
- Identify the central columns and rows that need to be mirrored:
c, d, f, g, i. - To maintain symmetry, consider adding black to
c, d, i.
By coloring squares c, d, i black, the figure will achieve two lines of symmetry: vertical and horizontal. This ensures that all sections mirror each other properly with the smallest number of additional black squares.
Therefore, the minimum number of boxes that must be colored black to achieve two lines of symmetry is c, d, i.
This strategy leverages the existing symmetry provided by the given black squares, minimizing the need for additional coloring.
Important Questions from Mirroring of Shapes
Examples of mirror and water reflections are shown in the figures below:
An object appears as the following image after first reflecting in a mirror and then reflecting on water.
The original object is
The mirror image of the above text about the X-axis is
The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ___________
- In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the transformed point will be
For the picture shown above, which one of the following is the correct picture representing reflection with respect to the mirror shown as the dotted line?
