Question

lmnopq is shown on the graph below. lmnopq is dilated by a scale factor of $\frac{1}{4}$ centered at $(2,2)$ to create $lmnopq$.
what is the perimeter of $lmnopq$?
write your answer as a whole number or as a decimal rounded to the nearest tenth.
units

Explanation:

Step1: Find the perimeter of \(LMNOPQ\)

• Calculate the lengths of the sides.
• Horizontal side \(LM\): The \(x\)-coordinate of \(L\) is \(-7\) and of \(M\) is \(-2\). Length \(LM=\vert-2 - (-7)\vert = 5\)
• Vertical side \(LQ\): The \(y\)-coordinate of \(L\) is \(2\) and of \(Q\) is \(-8\). Length \(LQ=\vert-8 - 2\vert = 10\)
• Since \(LMNOPQ\) is a rectangle (opposite sides equal), perimeter \(P = 2\times(5 + 10)=30\)

Step2: Apply the scale factor

• When a figure is dilated by a scale factor \(k=\frac{1}{4}\), the perimeter of the new figure \(P'\) is \(P'\) \(=k\times P\)
• Substitute \(k = \frac{1}{4}\) and \(P = 30\) into the formula: \(P'=\frac{1}{4}\times30 = 7.5\)

Answer:

\(7.5\)