Suppose an architect draws a segment on a scale drawing with the end points (0,0) and (3/4,9/10). the same segment on the actual structure has the end points (0,0) and (30,36). what proportion could model this situation?

Let the segment be represented by AB where A(0,0) = and B(3/4,9/10) = .

The length of the segment drawn by architect can be calculated using distance formula:

AB =

Similarly, Let the actual end points of segment be AC where A(0,0) = and C(30,36) = .

The length of the original segment can be calculated using distance formula:

AC =

.

Thus, the actual length is 40 times the length of the segment drawn by the architect.

Thus, the proportion of the model is 1:40

Answer with explanation:

Distance between two points (a,b) and (c,d) on two dimensional coordinate plane is given by

A=(0,0)

⇒P=(0,0) and Q= (30, 36)

⇒Actual Structure of segment =40 × Length of Segment on Scale