ΔEFI is dilated by a scale factor of one third with the center of dilation at point F. Then, it is reflected over line a to crea

Question

3 years ago

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ΔEFI is dilated by a scale factor of one third with the center of dilation at point F. Then, it is reflected over line a to crea

te ΔHFG. Based on these transformations, which statement is true?
Line segments EG and HI intersect at point F, forming triangles EFI and HFG. Line a intersects with both triangles at point F.

segment FE = segment FH over 3, segment FI = segment FG over 3, and segment EI = segment HG over 3; ΔEFI ~ ΔHFG

segment FE = segment FG over 3, segment FI = segment FH over 3, and segment EI = segment HG over 3; ΔEFI ~ ΔGFH

segment FE over 3 = segment FG, segment FI over 3 = segment FH, and segment EI over 3 = segment HG; ΔEFI ~ ΔGFH

segment FE over 3 = segment FH, segment FI over 3 = segment FG, and segment EI over 3 = segment HG; ΔEFI ~ ΔHFG

Mathematics

2 answers:

timofeeve [1] · Answer 1 · 2022-04-12T12:46:05+03:00

Answer:

The correct option is;

Segment FE over 3 = Segment FH

Segment FI over 3 = Segment FG, and

Segment EI over 3 = Segment HG

ΔEFI ~ ΔHFG

Step-by-step explanation:

The given transformations are'

ΔEFI is dilated by a scale factor of 1/3 and then it is reflected over line a

By dilation, we have

FH = 1/3×FE

FG = 1/3×FI

HG = 1/3×EI

Also by reflection over a line, the relative positions of the y-coordinates of the points remain the same while the x coordinates changes sign such that an upright mirror image of the dilated triangle is formed

Therefore, since we have;

$\dfrac{sin\alpha}{sin\beta } \ and \ \dfrac{sin\gamma}{sin\alpha }$ the same for both triangles, that is given the following relation;