Question

drag the tiles to the correct boxes to complete the pairs.
△abc and △pqr are similar. △abc is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point b to form △pqr. the side lengths of △abc are ab, 5 units, bc, 4.2 units, and ac, 4 units. match each side of △pqr to its length.
pq qr pr
5.25 units
5 units
6.25 units
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Explanation:

Step1: Recall the effect of dilation on side lengths

When a figure is dilated by a scale factor \(k\), the length of each side of the new figure is \(k\) times the length of the corresponding side of the original figure. Here, \(k = 1.25\).

Step2: Calculate the length of \(\overline{PQ}\)

Since \(\overline{PQ}\) corresponds to \(\overline{AB}\) (dilation and rotation preserve correspondence). Given \(AB=5\) units. Using the formula \(PQ=k\times AB\), we have \(PQ = 1.25\times5=\frac{5}{4}\times5=\frac{25}{4}=6.25\) units.

Step3: Calculate the length of \(\overline{QR}\)

Since \(\overline{QR}\) corresponds to \(\overline{BC}\). Given \(BC = 4.2\) units. Using the formula \(QR=k\times BC\), we have \(QR=1.25\times4.2=\frac{5}{4}\times\frac{42}{10}=\frac{210}{40}=5.25\) units.

Step4: Calculate the length of \(\overline{PR}\)

Since \(\overline{PR}\) corresponds to \(\overline{AC}\). Given \(AC = 4\) units. Using the formula \(PR=k\times AC\), we have \(PR = 1.25\times4=\frac{5}{4}\times4 = 5\) units.

Answer:

\(\overline{PQ}\to6.25\) units, \(\overline{QR}\to5.25\) units, \(\overline{PR}\to5\) units