Respuesta :
Let the segment be represented by AB where A(0,0) = [tex]A(x_{1}, y_{1})[/tex] and B(3/4,9/10) = [tex]B(x_{2}, y_{2})[/tex].
The length of the segment drawn by architect can be calculated using distance formula:
AB =[tex]\sqrt{}( x_{2}- x_{1})^ {2} + (y_{2}- y_{1})^ {2}[/tex]
[tex]AB=\sqrt{(3/4-0)^{2}+(9/10-0)^{2}[/tex]
[tex]AB=\sqrt{9/16+81/100} \\[/tex]
[tex]AB = (6\sqrt{61})/40[/tex]
Similarly, Let the actual end points of segment be AC where A(0,0) = [tex]A(x_{1}, y_{1})[/tex] and C(30,36) = [tex]C(x_{2}, y_{2})[/tex].
The length of the original segment can be calculated using distance formula:
AC =[tex]\sqrt{}( x_{2}- x_{1})^ {2} + (y_{2}- y_{1})^ {2}[/tex]
[tex]AC=\sqrt{(30-0)^{2}+(36-0)^{2}[/tex]
[tex]AC=\sqrt{900+1296} \\[/tex]
[tex]AC = (6\sqrt{61})[/tex].
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
[tex]=\sqrt{(a-c)^2+(b-d)^2}[/tex]
A=(0,0)
[tex]B=(\frac{3}{4},\frac{9}{10})\\\\AB=\sqrt{(\frac{3}{4}-0)^2+(\frac{9}{10}-0)^2}\\\\=\sqrt{\frac{9}{16}+\frac{81}{100}}\\\\=\sqrt{\frac{2196}{1600}}[/tex]
⇒P=(0,0) and Q= (30, 36)
[tex]PQ=\sqrt{(30-0)^2+(36-0)^2}\\\\PQ=\sqrt{900+1296}\\\\PQ=\sqrt{2196}\\\\\frac{PQ}{AB}=\frac{\sqrt{2196}}{\sqrt{\frac{2196}{1600}}}\\\\P Q=AB \times\sqrt{1600}\\\\PQ=40\times AB\\\\\frac{PQ}{AB}=40:1[/tex]
⇒Actual Structure of segment =40 × Length of Segment on Scale
