The red shape has been translated to the blue shape. the translation is a) (x', y') = (x, y - 6) b) (x', y') = (x - 6, y) c) (x', y') = (x - 4, y - 4) d) (x', y') = (x - 6, y - 6)

The translation that is done is:

Option: A (   A)(x', y') = (x, y - 6) )

Step-by-step explanation:

The red shape has been translated to the blue shape. We are asked to find the rule of the translation that is used to transform the image.

Clearly from the image and the pre-image we can see the transformation is occured as:

(5,0) → (5,-6)

(5,2) → (5,-4)

(3,4) → (3,-2)

(-3,4) → (-3,-2)

(-5,2) → (-5,-4)

(-5,0) → (-5,-6)

(-2,2) → (-2,-4)

(2,2) → (2,-4).

Hence, by seeing all the point of the image and pre-image we could clearly observe that the transformation that has taken place is the x-value of the coordinate remains unchanged and the y-value is reduced by 6.

i.e. (x,y) → (x,y-6)

i.e. (x',y')=(x,y-6).

Hence, option:  A is correct.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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