Get the answer to "Check whether the given dilationis a similarity transformation..."

pedzenekO

Answered question

2020-10-27

Check whether the given dilationis a similarity transformation or not.
Given:
The given dilation is

Answer & Explanation

Mayme

Skilled2020-10-28Added 103 answers

Calculation:
From the figure, the given vertices are
A(0,0),B(-4,-4),C(4,-2),D(-2,-2),E(2,-1)
Find the distance (using distance formula) of corresponding sides and find the ratio.

A B = \sqrt{{(- 4 - 0)}^{2} + {(- 4 - 0)}^{2}} = \sqrt{32} = 4 \sqrt{2}

A D = \sqrt{{(- 2 - 0)}^{2} + {(- 2 - 0)}^{2}} = \sqrt{8} = 2 \sqrt{2}

\frac{A D}{A B} = \frac{2 \sqrt{2}}{4 \sqrt{2}} = \frac{1}{2}

A C = \sqrt{{(4 - 0)}^{2} + {(- 2 - 0)}^{2}} = \sqrt{20} = 2 \sqrt{5}

A E = \sqrt{{(2 - 0)}^{2} + {(- 1 - 0)}^{2}} = \sqrt{5}

\frac{A E}{A C} = \frac{\sqrt{5}}{2 \sqrt{5}} = \frac{1}{2}

B C = \sqrt{{[4 - (- 4)]}^{2} + {[- 2 - (- 4)]}^{2}} = \sqrt{68} = 2 \sqrt{17}

D E = \sqrt{{[2 - (- 2)]}^{2} + {[- 1 - (- 2)]}^{2}} = \sqrt{17}

\frac{D E}{B C} = \frac{\sqrt{17}}{2 \sqrt{17}} = \frac{1}{2}

From the above result, the lenght of the sides are proportional.
By the use of SSS similarity,

△ A D E \sim △ A B C

.
Hence the given dilation is a similarity transformation.

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