We need to represent \[-sqrt(2)\] on the number line, \[1.\] With centre \[O\] and radius \[OB\], draw an arc cutting the number line at a point on the left side of \[O\]. \[2.\] At point \[A\], draw a perpendicular \[AB\] of length \[1\] unit. \[3.\] Mark a point \[A\] at \[x=-1\] and \[O\] at \[x=0\]. \[4.\] Join \[O\] to \[B\]. Which of the following is the correct order of steps of construction ? Choose 1 answer: A \[3-4-2-1\] B \[3-2-4-1\] C \[2-1-3-4\] D \[2-3-1-4\]

To represent $-\sqrt{2}$ on the number line, we need to construct a right-angled triangle with legs of length 1 unit. The hypotenuse of this triangle will have a length of $\sqrt{1^2 + 1^2} = \sqrt{2}$. We then transfer this length to the number line.

Let's analyze the given steps:

• Step 3: Mark a point A at x=-1 and O at x=0. This step establishes the origin (O) and a point A at -1, which will be used as one leg of our right triangle. This must be the first step.
• Step 2: At point A, draw a perpendicular AB of length 1 unit. After marking A, we can draw a perpendicular line segment AB of length 1 unit. This forms the second leg of our right triangle. This step must come after Step 3.
• Step 4: Join O to B. Now that we have points O and B, we can connect them to form the hypotenuse OB. The length of OB will be $\sqrt{OA^2 + AB^2} = \sqrt{1^2 + 1^2} = \sqrt{2}$. This step must come after Step 2.
• Step 1: With centre O and radius OB, draw an arc cutting the number line at a point on the left side of O. Finally, using O as the center and the length of the hypotenuse OB ($\sqrt{2}$) as the radius, we draw an arc that intersects the number line to the left of O. This point of intersection will represent $-\sqrt{2}$. This step must come last.

Therefore, the correct order of steps is 3-2-4-1.

The final answer is $B$