Math  /  Geometry

Question14. Pricrice suppose a trilangle wros ditated by a seale factor of s whith cemter of ailations? and the image of that diation was oivated by a scale factor of it with center of slation still at PP, What single tranisformation would havis the same effect on the originad triangle? luselfy your answer with an harge.

Studdy Solution
Justify the transformation mathematically:
Consider a point A A on the original triangle. After the first dilation, the image of A A is at A A' , such that A=P+s(AP) A' = P + s \cdot (A - P) . After the second dilation, the image of A A' is at A A'' , such that A=P+t(AP) A'' = P + t \cdot (A' - P) .
Substitute A A' into the equation for A A'' :
A=P+t((P+s(AP))P) A'' = P + t \cdot ((P + s \cdot (A - P)) - P) =P+t(s(AP)) = P + t \cdot (s \cdot (A - P)) =P+(s×t)(AP) = P + (s \times t) \cdot (A - P)
This shows that the single transformation is a dilation with scale factor s×t s \times t from the center P P .
The single transformation that has the same effect on the original triangle is a dilation with scale factor s×t s \times t from the center P P .

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