Question

a. is figure 2 a scaled copy of figure 1? yes or no? (1 pt)
b. what is the scale factor? if there is no scale factor, write “none.” show how you found if there is or is not a scale factor. (2 pts)
figure 1 (with grid, side 5, hypotenuse 6.4)
figure 2 (with grid, side 6, vertical side 3, hypotenuse 6.7)

Explanation:

Part a

Step1: Recall scaled copy definition

A scaled copy has proportional corresponding sides (and angles). For right triangles, check if \(\frac{\text{base of Figure 2}}{\text{base of Figure 1}}=\frac{\text{height of Figure 2}}{\text{height of Figure 1}}=\frac{\text{hypotenuse of Figure 2}}{\text{hypotenuse of Figure 1}}\).

Figure 1: base = 5, height = 4, hypotenuse = 6.4
Figure 2: base = 6, height = 3, hypotenuse = 6.7

Step2: Check ratios

Base ratio: \(\frac{6}{5} = 1.2\)
Height ratio: \(\frac{3}{4}=0.75\)
Hypotenuse ratio: \(\frac{6.7}{6.4}\approx1.047\)

Ratios are not equal, so not a scaled copy.

Step1: Check proportionality (from part a)

Since \(\frac{6}{5}
eq\frac{3}{4}
eq\frac{6.7}{6.4}\), the sides are not proportional.

Step2: Determine scale factor

A scale factor requires all corresponding linear measurements to be multiplied by the same value. Since ratios differ, no scale factor exists.

Answer:

No

Part b