On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral Q R S T has points (negative 1, 0), (5, 0), (3.5, negative 6) and (negative 2.5, negative 6). Quadrilateral Q prime R prime S prime T prime has points (negative 1, 2), (1, 2), (0.5, 0), and (negative 1.5, 0). Quadrilateral QRST is dilated and translated to form similar figure Q'R'S'T'. What is the scale factor for the dilation?

The given transformation of quadrilateral QRST to quadrilateral Q'R'S'T'

are a dilation and a translation, therefore,  QRST is similar to Q'R'S'T'.

Reasons:

The vertices of the quadrilateral are;

Quadrilateral QRST

Q(-1, 0)

R(5, 0)

S(3.5, -6)

T(-1, 2)

Quadrilateral Q'R'S'T'

Q'(-1, 2)

R'(1, 2)

S'(0.5, 0)

T'(-1.5, 0)

The given transformation that gives quadrilateral Q'R'S'T' from quadrilateral  QRST are a dilation and a translation.

Required:

The scale factor of the dilation

Solution:

Length of = 1 - (-1) = 2

Length of = 5 - (-1) = 6

Therefore;

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.

Step-by-step explanation:

In quadrilateral QRST, Q(-1,0), R(5,0), S(3.5,-6), T(-2.5,-6).

In quadrilateral Q'R'S'T', Q'(-1,2), R'(1,2), S'(0.5,0), T'(-1.5,0).

Distance formula:

Using distance formula , we get

Now,  

Therefore the scale factor is .

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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step-by-step explanation:

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