Question

sissy wants to enlarge a picture of a constellation so that she can put it on the wall in her daughters room what will be the area of the enlarged picture on the wall? 24 in² 108 in² 224 in² 486 in²

Explanation:

Step1: Find the scale factor

The original length \( LM = 4\) inches. The length from the center of dilation \(Q\) to \(LM\) is \(12\) inches, and the length from the center of dilation \(Q\) to \(L'M'\) is \(12 + 42=54\) inches.
The scale factor \(k=\frac{54}{12}=\frac{9}{2}\)

Step2: Find the dimensions of the enlarged rectangle

The original rectangle has length \(l = 4\) inches and width \(w = 6\) inches.
The enlarged length \(l'=4\times\frac{9}{2}=18\) inches.
The enlarged width \(w'=6\times\frac{9}{2}=27\) inches.

Step3: Calculate the area of the enlarged rectangle

The area of a rectangle \(A = l'\times w'\)
\(A=18\times27 = 486\) square inches

Answer:

\(486\ \text{in}^2\) (the fourth option)