Question

A 24 cm line AB is vertically standing on a horizontal plane. The station point is located 18 cm above ground and 15 cm in front of the line AB. The picture plane is located in between the line AB and station point perpendicular to the sight line. The distance between the picture plane and the station point is 9 cm. The height of the perspective view of the line AB is ________cm. (rounded off to one decimal place)

Hint:

When performing perspective drawing calculations, be sure to use formula involving the correct scaling factors. The method employed can be adjusted, with more

Answer 1

Given:
Line AB length = 24 cm
Station point height above ground = 18 cm
Distance from station point to line AB = 15 cm
Distance from station point to picture plane = 9 cm

Step 1: Apply the perspective view height formula:
\[{Height of perspective view} = \frac{h_1 \times d_2}{d_1 + d_2}\] Where:
\( h_1 = 18 \, {cm} \) (station point height)
\( d_1 = 15 \, {cm} \) (distance from station point to line AB)
\( d_2 = 9 \, {cm} \) (distance from station point to picture plane)

Step 2: Substitute values:
\[{Height of perspective view} = \frac{18 \times 9}{15 + 9} = \frac{162}{24} = 6.75 \, {cm}\] The calculated height is \( 6.75 \, {cm} \