Answer :
Answer:
[tex]\dfrac{1}{3}[/tex].
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:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula , we get
[tex]QR=\sqrt{(5-(-1))^2+(0-0)^2}=\sqrt{6^2}=6[/tex]
[tex]Q'R'=\sqrt{(1-(-1))^2+(2-2)^2}=\sqrt{2^2}=2[/tex]
Now,
[tex]\text{Scale factor}=\dfrac{Q'R'}{QR}[/tex]
[tex]\text{Scale factor}=\dfrac{2}{6}[/tex]
[tex]\text{Scale factor}=\dfrac{1}{3}[/tex]
Therefore the scale factor is [tex]\dfrac{1}{3}[/tex].
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'.
[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation\ between \ QRST \ and \ Q'R'S'T' \ is} \ \dfrac{1}{3}[/tex]
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:
[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{\mathrm{Length \ of \ \overline{Q'R'} }}{\mathrm{Length \ of \ \overline{QR}} }[/tex]
Length of [tex]\overline{Q'R'}} }[/tex] = 1 - (-1) = 2
Length of [tex]\overline{QR}} }[/tex] = 5 - (-1) = 6
Therefore;
[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{2}{6} = \dfrac{1}{3}[/tex]
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https://brainly.com/question/12077721