212k views
5 votes
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?

User Dennso
by
8.0k points

1 Answer

5 votes

Segment drawn on scale having end points O (0,0) and A
((3)/(4),(9)/(10)) is a line segment.

O A=
\sqrt{[(3)/(4) -0]^(2) +[(9)/(10) -0]^(2)\\\\

O A =
= \sqrt{(9)/(16)+(81)/(100)

=
\sqrt(549)/(400)

=
(√(549))/(20)

Now , the same segment actual structure having end points O'(0,0) and B (30,36) is also a line segment.

O'B=
\sqrt{(30-0)^(2)+(36-0)^(2)

=
√(900+1296)

=
\sqrt {2196}

= 2√549


\frac{\text{Actual length}}{\text{Length on scale}}=(OB')/(OA)=(2\sqrt549)/((\sqrt549)/(20))=40 [Cancelling √549 from numerator and denominator]

So, Actual length = 40 × Length on scale

User Beertastic
by
7.6k points