Question

a. draw a scaled copy of the polygon using a scale factor 3. label the copy a. b. draw a scaled copy of the polygon with a scale factor 1/2. label it b. c. is polygon a a scaled copy of polygon b? if so, what is the scale factor that takes b to a?

Explanation:

Step1: Recall scaling rule

To scale a polygon, multiply the coordinates of each vertex by the scale - factor.

Step2: Draw Polygon A

For a scale factor of 3, if the original polygon has vertices with coordinates $(x,y)$, the new vertices of Polygon A will have coordinates $(3x,3y)$. Plot these new vertices on the grid and connect them to form Polygon A.

Step3: Draw Polygon B

For a scale factor of $\frac{1}{2}$, if the original polygon has vertices with coordinates $(x,y)$, the new vertices of Polygon B will have coordinates $(\frac{1}{2}x,\frac{1}{2}y)$. Plot these new vertices on the grid and connect them to form Polygon B.

Step4: Find scale factor from B to A

Let the scale factor from B to A be $k$. If we know that Polygon B is scaled by $\frac{1}{2}$ from the original and Polygon A is scaled by 3 from the original. We can find $k$ by the ratio of the scale - factors of A and B with respect to the original polygon. So $k=\frac{3}{\frac{1}{2}} = 6$.

Answer:

A. Draw Polygon A by multiplying original vertex coordinates by 3.
B. Draw Polygon B by multiplying original vertex coordinates by $\frac{1}{2}$.
C. Yes, the scale factor from B to A is 6.