How to point root 2 on number line
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Step-by-Step Solution
Step 1: Draw a Number Line
First, draw a straight line and mark a point as 0. Then, mark another point to its right as 1, ensuring a unit distance between them. This establishes our scale on the number line.
Step 2: Construct a Perpendicular
At the point representing 1 on the number line, draw a line segment perpendicular to the number line. This segment should also have a length of 1 unit, matching the distance between 0 and 1.
Step 3: Form a Right-Angled Triangle
Now, connect the endpoint of the perpendicular segment (which is 1 unit above the point 1 on the number line) to the point 0 on the number line. This forms a right-angled triangle with two sides of length 1 unit.
Step 4: Apply Pythagorean Theorem
Using the Pythagorean theorem, the length of the hypotenuse of this right-angled triangle is 12+12=2. This hypotenuse represents the distance from 0 to the endpoint of the perpendicular.
Step 5: Plot on Number Line
With 0 as the center and the length of the hypotenuse (which is 2) as the radius, draw an arc that intersects the number line. The point where the arc intersects the positive side of the number line is the location of 2.