Question

HELP!11! WILL GIVE BRAINLIEST!

Your friend claims that if you dilate the pictured rectangle by a scale factor of three, then the area of your new rectangle will also increase by a factor of three. Is your friend correct? Explain your reasoning in at least three sentences. (Hint: Plot the points of both rectangles. Find the lengths and widths of both rectangles. Then find the area of both rectangles using the formula A = l x w .)

NOTE: MUST USE R.A.C.E. TO ANSWER

Answer 1

Answer:

The friend's claim is incorrect

if you dilate the pictured rectangle by a scale factor of three, then the area of your new rectangle will be 9 times the original area      

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor, and the ratio of its areas is equal to the scale factor squared

so

In this problem, the friend's claim is incorrect

The scale factor is 3

The scale factor squared is 3^2=9

so

if you dilate the pictured rectangle by a scale factor of three, then the area of your new rectangle will be 9 times the original area

Verify

The dimensions of the original rectangle ABCD are

AB=6 unis

BC=4 units

The original area is

A=(6)(4)=24 units^2

If the scale factor is 3

The new dimensions are

A'B'=6*3=18 unis

B"C'=4*3=12 units

The new area is

A'=(18)(12)=216 units^2

Divide the areas

216/24=9

therefore

The new area is 9 times the original area