Question

ABC is rotates 180 degrees about the origin and then dilated by a factor of 1/2 using the point (4,6) as the center of dilation. What is the transformational c(2,4)?

Answer 1

Answer:

A.   C" (1, 1).

Step-by-step explanation:

The rotation takes C  (2, 4) to the  point  C' (-2, -4).

The dilation of 1/2  centered at (4, 6)  will take this new point C' to the midpoint of (4, 6) and (-2, -4)  which is (4 - 2)/2,  (-4+6)/2 = (1, 1)  = C" (answer).

Answer 2

The transformational C(2,4) is C"(1, 1) .

What is meaning of Dilation?

Dilation means to change the size of the object keeping the image same , The figure can be made bigger or smaller but the initial image remains same.

It is given in the question that

The given figure ABC  is rotated 180 degrees about the origin

then dilated by a factor of 1/2 , using the point (4,6) as the center of dilation

The  180 degrees rotation takes so C  (X,Y) to the  point  C' (-X, -Y)

So , C(2, 4) to C (-2 , -4)

The dilation factor =  1/2  centered at (4, 6)  

will take this new point C' to the midpoint of (4, 6) and (-2, -4)

It will be

(4 - 2)/2 ---> X = 1

(-4+6)/2 -----> Y = 1

C"(1, 1)  

Therefore the transformational C(2,4) is C"(1, 1) .

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