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

the rectangle pqrs is a dilation of the rectangle pqrs. 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 pqrs is a dilation of the rectangle pqrs. 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

Explanation:

Step1: Find side - lengths of original and dilated rectangles

Let's consider the horizontal sides. For rectangle $PQRS$, if we assume $P(-4,3)$ and $Q(6,3)$, the length of $PQ$ is $|6 - (-4)|=10$. For rectangle $P'Q'R'S'$, if $P'(-4,4)$ and $Q'(8,4)$, the length of $P'Q'$ is $|8 - (-4)| = 12$.

Step2: Calculate the 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, $k=\frac{\text{length of side of }P'Q'R'S'}{\text{length of side of }PQRS}=\frac{12}{10}=\frac{6}{5}$.

Answer:

$\frac{6}{5}$