Question

Draw a line segment $ XY = 9cm $ . Draw $ AB \bot XY $ , such that $ XB = BY = 4.5cm $

Answer 1

Hint: Firstly, draw a line and then mark two points $ X $ and $ Y $ with a distance of $ 9cm $ between them. This becomes our line segment $ XY $ . Now, we have to follow certain steps in order to construct a perpendicular $ AB $ satisfying the given conditions.

Complete step-by-step answer:
Step 1: First, let us draw a line as follows.

Now, we place one point $ X $ on this line.

Now, let us take a compass and measure $ 9cm $ on it and draw an arc on the above line with $ X $ as the centre.

This intersection point would be $ Y $ . Therefore, this becomes the line segment $ XY $ of length $ 9cm $

Step 2: Now we have to draw a line $ AB $ perpendicular to this line segment such that $ XB = BY = 4.5cm $
In order to do this, we first place a point on the line segment which cuts the line segment in half and let this point be $ B $

This point $ B $ is equidistant from both the points $ X $ and $ Y $ of the line segment. Now, using a protractor with the point $ B $ as its centre, mark a point at $ 90 $ degrees. We name this point to be $ A $

Now, we join the points $ A $ and $ B $ to form a perpendicular. Hence, this perpendicular is shown as

Therefore, This line $ AB $ is the perpendicular of the line segment $ XY $ such that $ XB = BY = 4.5cm $

Note: Note that we can also draw this perpendicular using a compass. This method is used if the question is to draw a perpendicular without using a protractor and involves several steps. In this case, since a perpendicular forms $ 90 $ degrees with the line segment, we use a protractor to mark a point at $ 90 $ degrees.