the rectangle ijkl is a dilation of the rectangle ijkl. what is the scale factor of the dilation? simplify…

the rectangle ijkl is a dilation of the rectangle ijkl. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

the rectangle ijkl is a dilation of the rectangle ijkl. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Answer

Answer:

$\frac{1}{2}$

Explanation:

Step1: Find side - length of original rectangle

The length of side $IJ$ of rectangle $IJKL$: The coordinates of $I(8,2)$ and $J(0,2)$. Using the distance formula for points on a horizontal line $d = |x_2 - x_1|$, we have $IJ=|8 - 0| = 8$.

Step2: Find side - length of dilated rectangle

The length of side $I'J'$ of rectangle $I'J'K'L'$: The coordinates of $I'(4,1)$ and $J'(0,1)$. Using the distance formula for points on a horizontal line $d = |x_2 - x_1|$, we have $I'J'=|4 - 0| = 4$.

Step3: Calculate scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So $k=\frac{I'J'}{IJ}=\frac{4}{8}=\frac{1}{2}$.