Question

suppose pentagon abcde undergoes a dilation by a scale factor of 2 to produce pentagon abcde. which statements are correct? a (overline{ab}approx5.66) b (overline{bc}approx9.32) c (overline{cd}=8)

Explanation:

Step1: Calculate the length of \( \overline{AB} \)

Using the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Let \( A=(x_1,y_1)=(5,9) \) and \( B=(x_2,y_2)=(7,7) \).
\( AB=\sqrt{(7 - 5)^2+(7 - 9)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83 \)
After dilation with scale factor \( k = 2 \), \( A'B'=k\times AB=2\times\sqrt{8}\approx5.66 \)

Step2: Calculate the length of \( \overline{BC} \)

Let \( B=(7,7) \) and \( C=(5,3) \).
\( BC=\sqrt{(5 - 7)^2+(3 - 7)^2}=\sqrt{4 + 16}=\sqrt{20}\approx4.47 \)
After dilation with scale factor \( k = 2 \), \( B'C'=k\times BC=2\times\sqrt{20}\approx8.94
eq9.32 \)

Step3: Calculate the length of \( \overline{CD} \)

Let \( C=(5,3) \) and \( D=(3,3) \).
\( CD=\sqrt{(3 - 5)^2+(3 - 3)^2}=\sqrt{4+0}=2 \)
After dilation with scale factor \( k = 2 \), \( C'D'=k\times CD=2\times2 = 4
eq8 \)

Answer:

A. \( \overline{A'B'}\approx5.66 \)