The figure below shows 12 identical squares. What is the least number of such squares that must be added to the figure so that the line ABAB becomes a line of symmetry?

Work through it with AI →

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

7

1. Identify the reflection of each column across the line of symmetry $AB$.

For the line ABAB to be a line of symmetry, every square above ABAB must have a corresponding square below ABAB at the same distance, and vice versa.

  • Row U1 reflects to Row D1.
  • Row U2 reflects to Row D2.

2. Determine the missing squares in each column.

  • Column 1: Has a square at U1, so it needs a square at D1 (11 square needed).
  • Column 2: Has squares at U2, U1, D1, D2. It is already symmetric.
  • Column 3: Has squares at U2, U1, D1, D2. It is already symmetric.
  • Column 4: Has squares at U1, D1. It is already symmetric.
  • Column 5: Has a square at D1, so it needs a square at U1 (11 square needed).

3. Calculate the total number of squares to be added.

Total squares to add =1+1=2= 1 + 1 = 2.

Answer

22 (option 2)

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.

More questions on this topic

  1. 1The figure below is made up of 2 squares, ABCD and DEFG. X is a point on GD and Y is a point on DE. BC = 7 cm, FE = 6 cm…
  2. 2The net drawn for the solid shown below is incorrect. Name the solid. Ans: (a)___ Shade a triangular face on the net tha…
  3. 3In the figure below, ABCD is a trapezium and AD = BC. Each of the statements is either true, false or not possible to te…
  4. 4In the figure, WXYZ is a trapezium and AXYB is a rhombus. XBC and XAZ are straight lines. WX // ZY, BC = BY, ∠XAB=82∘\angle XAB = 82^\circ…
  5. 5It is given that ξ={x:x is polygon},\xi = \{x: x \text{ is polygon}\}, p={x:x is a parallelogram},p = \{x: x \text{ is a parallelogram}\}, q={x:x is a quadrilateral},q = \{x: x \text{ is a quadrilateral}\},…