Question

problem 2 figure efgh is a scaled copy of figure abcd. select the true statements. the length of segment ad is 8 units. the scale factor from efgh to abcd is 2. the area of efgh is twice the area of abcd. the ratio of ab/bc is equivalent to the ratio of eh/hg.

Explanation:

Step1: Analyze side - length of AD

By observing the blue figure ABCD, using the distance formula for two - dimensional points (or simply counting grid units if applicable), we find that using the Pythagorean theorem for right - triangle formed by the sides of the figure with vertices A and D. The vertical distance from A to a point on the same horizontal line as D is 4 and the horizontal distance is 6. So, $AD=\sqrt{3^{2}+4^{2}} = 5
eq8$.

Step2: Calculate scale factor

The ratio of corresponding side lengths gives the scale factor. For example, if we take side CD = 6 in ABCD and side GH = 12 in EFGH, the scale factor from ABCD to EFGH is $\frac{GH}{CD}=\frac{12}{6}=2$, so the scale factor from EFGH to ABCD is $\frac{1}{2}
eq2$.

Step3: Analyze area relationship

If the scale factor between two similar figures is $k$, the ratio of their areas is $k^{2}$. Since $k = 2$ from ABCD to EFGH, the area of EFGH is $k^{2}=4$ times the area of ABCD, not 2 times.

Step4: Check ratio of side - length ratios

For similar figures, the ratios of corresponding side - lengths are equal. In similar figures ABCD and EFGH, $\frac{AB}{BC}=\frac{3}{4}$ and $\frac{EH}{HG}=\frac{16}{12}=\frac{4}{3}$, they are not equal.

Answer:

None of the statements are true.