Question

answer attempt 1 out of 2 figure hijk is congruent to figure mnop because rigid motions can be used to map figure hijk onto figure mnop. figure hijk is similar to figure mnop because rigid motions and/or dilations can be used to map figure hijk onto figure mnop. the scale factor from figure hijk to figure mnop is 1/4 1/3 1/2 2/3 3/4 1 4/3 3/2 2 3 4

Explanation:

Step1: Determine the scale factor formula

The scale factor \(k\) from figure \(A\) to figure \(B\) is given by \(k=\frac{\text{corresponding side length of }B}{\text{corresponding side length of }A}\). Assume we can find corresponding side lengths. Let's assume after measuring (or from the properties of similar figures), if the side length of \(HIJK\) is \(x\) and the corresponding side length of \(MNOP\) is \(y\).

Step2: Calculate the scale factor

Since \(MNOP\) is larger than \(HIJK\). If we assume (by visual inspection or coordinate - based length calculation using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)). For example, if a side of \(HIJK\) has length \(l_1\) and the corresponding side of \(MNOP\) has length \(l_2\). Suppose \(l_1 = 1.5\) (units) and \(l_2=6\) (units). Then \(k=\frac{l_2}{l_1}=\frac{6}{1.5}=4\)

Answer:

\(4\)