The scale factor used to create triangle ΔJ'K'L', is 3
The reason for arriving at the above scale factor is as follows;
The known parameters:
The vertices of the triangle ΔJKL are:
J(2, 4), K(3, 2), and L(4, 3)
The vertices of the triangle ΔJ'K'L' are:
J'(6, 12), K'(9, 6), and L'(12, 9)
The required parameter:
The scale factor used to create ΔJ'K'L'
The strategy:
Find and divide the lengths of the sides of ΔJ'K'L', by the calculated lengths of the sides of the triangle ΔJKL as follows;
The lengths of the segments in ΔJKL are;
JK = √((3 - 2)² + (2 - 4)²) = √5
KL = √((4 - 3)² + (3 - 2)²) = √2
JL = √((4 - 2)² + (3 - 4)²) = √5
The lengths of the segments in ΔJ'K'L' are;
J'K' = √((9 - 6)² + (6 - 12)²) = √(45) = 3·√5
K'L' = √((12 - 9)² + (9 - 6)²) = √(18) = 3·√2
J'L' = √((12 - 6)² + (9 - 12)²) = √(45) = 3·√5
Therefore, we get;
[tex]\mathbf{Scale \ factor, \ S.F. = \dfrac{J'K'}{JK} = \dfrac{K'L'}{KL} = \dfrac{J'L'}{JL} = 3}[/tex]
The scale factor used to create triangle triangle ΔJKL from triangle ΔJ'K'L' , S.F. = 3
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