Question

the scale factor from the original figure to its copy is $\frac{3}{2}$. draw the original figure.

Explanation:

Step1: Recall scale - factor formula

If the scale factor from the original to the copy is $k=\frac{3}{2}$, then the dimensions of the original $x$ and the copy $y$ are related by $y = kx$. To find the original dimensions, we use $x=\frac{2}{3}y$.

Step2: Analyze copy's dimensions

Count the side - lengths of the copy on the grid. Let's assume the horizontal and vertical side - lengths of the rectangles in the copy. For example, if a horizontal side of a rectangle in the copy is 3 units long, then the corresponding horizontal side of the original is $3\times\frac{2}{3}=2$ units long. If a vertical side of a rectangle in the copy is 2 units long, then the corresponding vertical side of the original is $2\times\frac{2}{3}=\frac{4}{3}$ units long. We can use the grid to draw the original figure by reducing each side - length of the copy by the factor of $\frac{2}{3}$.

Answer:

Draw a figure on the grid where each side - length is $\frac{2}{3}$ of the corresponding side - length of the given copy figure. For example, if a side of the copy is 3 grid - squares long, the corresponding side of the original is 2 grid - squares long.