Question

the trapezoid ( hijk ) is a dilation of the trapezoid ( hijk ). what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find length of IJ

IJ is vertical: distance between I(-2,2) and J(-2,-1) is $2 - (-1) = 3$? No, wait, check green IJ': I'(-8,8), J'(-8,-4). IJ' length: $8 - (-4) = 12$. Blue IJ: I(-2,2), J(-2,-1)? Wait no, blue J is (-2,-1)? Wait blue IJ: vertical segment from I(-2,2) to J(-2,-1)? Length is 3. Green IJ': from I'(-8,8) to J'(-8,-4): length is 12. Scale factor = image length/original length = 12/3 = 4. Or check horizontal segments: blue HK: from H(0,2) to K(2,-1)? No, blue JK is horizontal from J(-2,-1) to K(2,-1): length 4. Green J'K'? Wait green J'(-8,-4) to K'(8,-4): length 16. 16/4=4. Correct.

Step2: Calculate scale factor

Scale factor = $\frac{\text{Length of } I'J'}{\text{Length of } IJ} = \frac{12}{3} = 4$

Answer:

4