Question

the two polygons in the image are scaled copies. explain how to find the scale factor in this diagram. use the lengths of the corresponding sides in your explanation on how to determine the scale factor. you can start your response with: • the scale factor for the polygons is... • i found my answer by... a polygon and its scaled copy

Explanation:

To find the scale factor, first identify corresponding sides of the two scaled polygons. For example, look at a side of the original polygon (e.g., side \( AB \)) and the corresponding side of the scaled copy (e.g., side \( EF \)). Measure (or determine from the grid) the lengths of these corresponding sides. Let the length of the original side be \( L_{original} \) and the length of the scaled side be \( L_{scaled} \). The scale factor \( k \) is calculated as \( k=\frac{L_{scaled}}{L_{original}} \) (if the scaled copy is an enlargement) or \( k = \frac{L_{original}}{L_{scaled}} \) (if it's a reduction). For instance, if \( AB \) has a length of 2 units (from the grid) and \( EF \) has a length of 4 units, the scale factor would be \( \frac{4}{2}=2 \), meaning the scaled copy is an enlargement by a factor of 2.

Answer:

To find the scale factor, identify corresponding sides of the two scaled polygons. Measure (or determine from the grid) their lengths. The scale factor is the ratio of the length of a side of the scaled copy to the length of the corresponding side of the original polygon (or vice versa, depending on enlargement/reduction). For example, if a side of the original is \( l_1 \) and the corresponding side of the copy is \( l_2 \), scale factor \( = \frac{l_2}{l_1} \) (for enlargement) or \( \frac{l_1}{l_2} \) (for reduction).