Question

5. The two figures are scaled copies of each other.

Answer 1

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 $\dfrac{1}{3}$

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 $\overline{AD}$ = √(2² + 3²) = √(13)

Length of $\overline{PS}$ = √(6² + 9²) = √(117) = √(9 × 13) = 3·√(13)

Therefore;

a. The scale factor that takes Figure 1 to Figure 2, SF₁₂, is therefore;

$SF_{12} = \mathbf{\dfrac{\overline{PS}}{\overline{AD}}}$

Which gives;

$SF_{12} = \dfrac{3 \cdot \sqrt{13} }{\sqrt{13} } = 3$

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;

$SF_{21} = \mathbf{\dfrac{\overline{AD}}{\overline{PS}}}$

Which give;

$SF_{21} = \dfrac{\sqrt{13} }{3 \cdot \sqrt{13} } = \mathbf{\dfrac{1}{3}}$

The scale factor that takes Figure 2 to Figure 1, SF₂₁ is $\underline{\dfrac{1}{3}}$

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