A Ferrari is used as the basis to make a toy model. Compare the two images. Determine the scale factor used to create the toy model.

Question option's

1

12

1/12

5/8

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For the image shown, what is the scale factor?

Question options:

3

4

1/3

1/4

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Is Quadrilateral DEFG~ Quadrilateral MNOP? Explain why or why not.

Question option's

No, because all corresponding angles are not congruent

No, because all corresponding sides are not proportional.

No, because all corresponding angles are not congruent and all corresponding sides are not proportional.

Yes, because all corresponding angles are congruent and all corresponding sides are proportional.

ForgottenMoon
Jun 2, 2018

#1**+2 **

Question 1:

Convert 5ft and 8ft to inches- 60 inches and 96 inches, respectively.

Other car: 5 inches and 8 inches

So, 60/5=12, and 96/8=12

Therefore, the answer is \(\boxed{\frac{1}{12}}\)

tertre
Jun 2, 2018

#2**+2 **

tertre, you have to be extremely vigilant toward the language used for this problem. Let's peruse it together, shall we?

"A Ferrari is used as the basis to make a toy model. Compare the two images. Determine the scale factor used to create the toy model."

The problem seeks the scale factor from the Ferrari to the toy model--not the toy model to the Ferraro. The toy model is smaller than the Ferrari, so the scale factor would have to be less than 1.

Do not worry, though! The scale factor would be the reciprocal of the answer you provided, 1/12.

TheXSquaredFactor
Jun 2, 2018

#3**0 **

I noticed that you repeated questions, and Omi67 answered your second question here: https://web2.0calc.com/questions/for-the-image-shown-what-is-the-scale-factor

Anyway, I guess I will help you with the third problem.

Notice that all the corresponding angles have the measure and are, therefore, congruent, by the Definition of Congruent Angles. For example, \(m\angle D=m\angle M\) and they are corresponding angles.

If corresponding sides are proportional, then this means that each ratio is equivalent. Pairs of corresponding sides include \(ED, NM\text{ and }DG,MP\text{ and }GF,PO\text{ and }FE,ON\) . The ratio of these sides must be the same in order for both quadrilaterals to be considered similar. Let's check that!

Does \(\frac{ED}{NM}=\frac{DG}{MP}=\frac{GF}{PO}=\frac{FE}{ON}\) ? Well, let's see!

Yes, \(\frac{3}{7.5}=\frac{6}{15}=\frac{12}{30}=\frac{9}{22.5}\) . This means that corresponding sides are proportional. Therefore, yes, \(DEFG\sim MNOP\)

TheXSquaredFactor
Jun 3, 2018