Q. 44.0( 297 Votes )

Represent on the number line.

Answer :

Step 1: Draw a line segment AB of 9.3 unit. Then, extend it to C so that BC = 1 unit.

Step 2: Now, AC = 10.3 units. Find the center of AC and mark it as O


Step 3: Draw a semi-circle with radius OC and center O.


Step 4: Draw a perpendicular line BD to AC at point B intersecting the semi-circle at D. And then, join OD


Step 5: Now, OBD is a right angled triangle


Here, OD (Radius of semi-circle)


OC 


BC = 1


Then,  OB = OC – BC


Using Pythagoras theorem,


OD2 = BD2 + OB2


()2 = BD2 + ()2


BD2 = ()2 - ()2


BD2 = ( ) ( + )


BD2 = 9.3


BD=


Thus, the length of BD is


Step 6: Taking BD as radius and B as the center, construct an arc which touches the line segment.


Now, the point where it touches the line segment is at a distance of from O as shown in the figure below


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