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AABC and APQR are similar. AABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form APQR. Match each side of PQR to its length.

a) PQ - 5.25 units
b) PR - 5 units
c) QR - 6.25 units
d) None of the above

User Sinh Phan
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1 Answer

4 votes

Final answer:

To find the lengths of the sides of △PQR, multiply the corresponding sides of △ABC by the scale factor 1.25. The 45° counterclockwise rotation affects orientation, not side lengths. Without the specific lengths of △ABC, we can't definitively match the lengths given to sides PQ, PR, or QR.

Step-by-step explanation:

The subject of the question is mathematics, specifically geometry dealing with similar triangles, dilations, and rotations. Given that △ABC and △PQR are similar and that △ABC is dilated by a scale factor of 1.25 to form △PQR, the lengths of the sides of △PQR can be determined by multiplying the corresponding sides of △ABC by this scale factor.

The rotation of the triangle 45° counterclockwise about point B does not change the lengths of the sides, it only changes the orientation of the triangle. Therefore, if we are given the lengths of the sides of △ABC, we simply scale those lengths by 1.25 to find the lengths of the sides of △PQR. Without knowing the specific lengths of △ABC, we cannot match the side lengths of △PQR to options (a), (b), or (c). However, the process is to multiply each side of △ABC by 1.25. If any side of △ABC had a length that when multiplied by 1.25 matches the lengths given in the options, then we would have our answer.

User Medel
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