If the scaling factor of quadrilateral E'F'G'H' with respect to quadrilateral EFGH is 1/3, determine the length of the sides of quadrilateral E'F'G'H'.

We use a scaling factor. Examine the similar triangles ABC and A'B'C' in the figure below.

If we calculate the ratios AB/A'B', BC/B'C', and CA/C'A', we see that each of these ratios is equal to 2. We call this common ratio the scaling factor of ΔABC with respect to ΔA'B'C'. If we calculate the reciprocal ratios A'B'/AB, B'C'/BC, and C'A'/CA, we see that each of these ratios is equal to 1/2. We call this common ratio the scaling factor of ΔA'B'C' with respect to ΔABC. Every pair of similar figures has two scaling factors that show the relationship between the corresponding side lengths.

If the scaling factor of quadrilateral E'F'G'H' with respect to quadrilateral EFGH is 1/3, determine the length of the sides of quadrilateral E'F'G'H'.

Transcribed Image Text:

21 F' 12 9. G' Н" н 9 G 10 A'r 5 3 B C' 4 B'