The quadrilaterals are similar and are related by a scale factor, taken from
a specific location, that maps the points on one figure to the other.
a. The scale factor that takes Figure 1 to Figure 2, is 3
b. The scale factor that takes Figure 2 to Figure 1 is [tex]\dfrac{1}{3}[/tex]
Reasons:
From the question, we have that Figure 1 is a scaled copy of Figure 2, therefore;
Let ABCD represent Figure 1, we have;
ABCD ~ PQRS
Length of [tex]\overline{AD}[/tex] = √(2² + 3²) = √(13)
Length of [tex]\overline{PS}[/tex] = √(6² + 9²) = √(117) = √(9 × 13) = 3·√(13)
Therefore;
a. The scale factor that takes Figure 1 to Figure 2, SF₁₂, is therefore;
[tex]SF_{12} = \mathbf{\dfrac{\overline{PS}}{\overline{AD}}}[/tex]
Which gives;
[tex]SF_{12} = \dfrac{3 \cdot \sqrt{13} }{\sqrt{13} } = 3[/tex]
The scale factor that takes Figure 1 to Figure 2, SF₁₂ = 3
(3 times the lengths of Figure 1 gives the lengths on Figure 2)
b. The scale factor that takes Figure 2 to Figure 1, SF₂₁, is given as follows;
[tex]SF_{21} = \mathbf{\dfrac{\overline{AD}}{\overline{PS}}}[/tex]
Which give;
[tex]SF_{21} = \dfrac{\sqrt{13} }{3 \cdot \sqrt{13} } = \mathbf{\dfrac{1}{3}}[/tex]
The scale factor that takes Figure 2 to Figure 1, SF₂₁ is [tex]\underline{\dfrac{1}{3}}[/tex]
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