Find the scale factor of trapezoid \mathrm{Q}\mathrm{R}\mathrm{S}\mathrm{T}QRST if it is dilated to \mathrm{Q}^{'} \mathrm{R}^{'} \mathrm{S}^{'} \mathrm{T}^{'}Q ′ R ′ S ′ T ′ . Type your result in the empty box provided below.
Answers
Question:
Find the scale factor of trapezoid [tex]\mathrm{Q}\mathrm{R}\mathrm{S}\mathrm{T}[/tex] if it is dilated to [tex]\mathrm{Q}^{'} \mathrm{R}^{'} \mathrm{S}^{'} \mathrm{T}^{'}[/tex].
Type your result in the empty box provided below.
Answer:
The scale factor is 2
Step-by-step explanation:
Given
See attachment for plots
Required
Determine the scale factor
Using QR and Q'R' as points of reference.
From the attached plot, we have:
[tex]QR = 4\ units[/tex]
[tex]Q'R' = 8\ units[/tex]
The scale factor (k) from [tex]\mathrm{Q}\mathrm{R}\mathrm{S}\mathrm{T}[/tex] to [tex]\mathrm{Q}^{'} \mathrm{R}^{'} \mathrm{S}^{'} \mathrm{T}^{'}[/tex]. is:
[tex]k = \frac{Q'R'}{QR}[/tex]
[tex]k = \frac{8\ units}{4\ units}[/tex]
[tex]k =2[/tex]
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[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{3x = 9}[/tex]
[tex]\large\text{DIVIDE 3 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{3x}{3}=\dfrac{9}{3}}[/tex]
[tex]\large\text{CANCEL out: } \mathsf{\dfrac{3}{3}} \large\text{ because that gives you 1}[/tex]
[tex]\large\text{KEEP: } \mathsf{\dfrac{9}{3}}\large\text{ because that helps us solve for x }[/tex]
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[tex]\boxed{\boxed{\large\textsf{Therefore, your \underline{answer} is: \huge \bf x = 3 }}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
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