Question

Using a protractor, draw $ \angle BAC $ of measure $ 70{}^\circ $ . On side $ AC $ , take a point $ P $ , such that $ AP=2 $ cm. From $ P $ draw a line perpendicular to $ AB $ .

Answer 1

Hint: First we need to construct a horizontal line on that line we will consider points $ A $ , $ C $ . From the point $ A $ we need to construct a line that is making an angle $ 70{}^\circ $ by using the protractor. On the inclined line, we will mark the point $ B $ . So that we have constructed the angle $ \angle BAC $ of measure $ 70{}^\circ $ . up to this half of the problem is completed, now we will move to the further section, which is to construct a perpendicular line to $ AB $ from point $ P $ where $ AP=2 $ cm. Now we will mark a point $ P $ on the horizontal line $ AC $ . Now from point $ P $ we will construct an arc with some radius and intersect the line $ AC $ at two points, from the two points, we will construct another two arcs without changing the radius now will connect the intersection point of the two curves and the point $ P $ .

Complete step by step answer:
Let us construct a horizontal line as shown in the below figure.

Now consider the points $ A, C $ on the above horizontal line.

Now we will take the protractor and place it on the point $ A $ , such that the horizontal line in the protractor coincides with the line passing through the point $ A $ and the middle point of the protractor also coincides with the point $ A $ . Now we will mark a point $ B $ at $ 70{}^\circ $ by observing the readings on the protractor and we will join the points $ A $ and $ B $ .

Now we need to construct the perpendicular line to the line $ AB $ from point $ P $ such that $ AP=2 $ cm. For this we are marking the point $ P $ on the line $ AC $ , such that $ AP=2 $ cm.

Now we will construct an arc from the point $ P $ with some radius which will bisect the line $ AB $ at two points.

Now with the same radius and taking centers as $ E $ and $ F $ , we will construct another two arcs which will intersect at one side of the line $ AB $ .

Now joining the intersection point and the point $ P $ , then we will get the required line.

Note:
 We can check the perpendicularity of the constructed line by calculating the angle made by the perpendicular line on the given line. For this type of construction, we need to have some accuracy and don’t disturb the equipment while drawing.