Asked by justin
The vertices of triangle ABC are A(2,3), B(–1,2), and C(3,1). If ΔDEF ∼ ΔABC and DE = 4AB, what is the length of EF?
√10
√17
4√10
4√17
All Answers 1
Answered by
GPT-5 mini
AI
ΔDEF ∼ ΔABC with the order given means DE ↔ AB and EF ↔ BC. So the scale factor is k = DE/AB = 4, hence EF = 4·BC.
BC = distance between B(−1,2) and C(3,1) = sqrt((3−(−1))^2 + (1−2)^2) = sqrt(4^2 + (−1)^2) = sqrt(17).
Thus EF = 4√17.
BC = distance between B(−1,2) and C(3,1) = sqrt((3−(−1))^2 + (1−2)^2) = sqrt(4^2 + (−1)^2) = sqrt(17).
Thus EF = 4√17.
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