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2 years ago

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A dilation with center O and scale factor r takes A to A' and B to B'. a) Explain how to find the center O b) If AB=6 mm and A'B

'= 15mm, calculate the scale factor r. c) Apply the Dilation theorem

1 answer:

vova2212 [387]2 years ago

8 0

Answer:

A.) Extending the line of multiple of scale factor r on two corresponding vertex

B.) Scale factor r = 2.5

C.) A'B'/AB = 5/2

Step-by-step explanation:

A.) To find the centre O, take a corresponding vertex of the two shapes. Draw a line passing through the the vertex and extending beyond the initial one. The length of the line must be multiplied by the scale factor r

The center of a dilation is a fixed point in the plane in which all points are expanded or contracted.

B.) If AB=6 mm and A'B'= 15mm,

The scale factor r = 15/6 = 5/2 = 2.5

C.) A'B'/AB = 5/2

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${\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}$

$\star \: \tt \cot \theta = \dfrac{7}{8}$

${\large{\textsf{\textbf{\underline{\underline{To \: Evaluate :}}}}}}$

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${\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}$

Consider a $\triangle$ ABC right angled at C and $\sf \angle \: B = \theta$

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$\longrightarrow \tt \cos \theta = \purple{ \dfrac{7}{ \sqrt{113} } }$

<u>Solving the given expression</u><u> </u><u>:</u><u>-</u><u> </u>

$\longrightarrow \: \tt \dfrac{(1 + \sin \theta)(1 - \sin \theta) }{(1 + \cos \theta) (1 - \cos \theta) }$

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$\begin{gathered} {\underline{\rule{300pt}{4pt}}} \end{gathered}$

${\large{\textsf{\textbf{\underline{\underline{We \: know :}}}}}}$

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${\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}$

✧ Figure in attachment

$\begin{gathered} {\underline{\rule{200pt}{1pt}}} \end{gathered}$

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