Question

quadrilateral pqrs is dilated by a scale factor of \\(\frac{3}{4}\\) to form quadrilateral pqrs. what is the measure of side sp? \
(image of quadrilateral pqrs with sides: sp = 24, pq = 24, qr = 48, rs = 33.9)

Explanation:

Step1: Recall the dilation formula

When a figure is dilated, the length of a side of the new figure \(L'\) is given by \(L'=L\times k\), where \(L\) is the length of the corresponding side of the original figure and \(k\) is the scale factor.

Step2: Identify the original side length and the scale factor

From the problem, the original side length \(SP = 24\) (since \(PQ = 24\) and in a dilation, corresponding sides are considered. Here \(SP\) corresponds to \(S'P'\)), and the scale factor \(k=\frac{3}{4}\).

Step3: Calculate the length of \(S'P'\)

Substitute \(L = 24\) and \(k=\frac{3}{4}\) into the formula \(L'=L\times k\). So \(S'P'=24\times\frac{3}{4}\).

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Answer:

\(18\)