Question

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?

Answer 1

Segment drawn on scale having end points O (0,0) and A $(\frac{3}{4},\frac{9}{10})$ is a line segment.

O A= $\sqrt{[\frac{3}{4} -0]^{2} +[\frac{9}{10} -0]^{2}$

O A = $= \sqrt{\frac{9}{16}+\frac{81}{100}$

     = $\sqrt\frac{549}{400}$

    = $\frac{\sqrt{549}}{20}$

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

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

     = $\sqrt{900+1296}$

     = $\sqrt {2196}$

     = 2√549

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

So, Actual length = 40 × Length on scale