Answer: Second option.
Step-by-step explanation:
First it is important to remember the definition of Dilation.
A Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure, before the transformation) have the same shape, but their sizes are different.
In this case you know that the triangle ABC is dilated by a scale factor of 2 with a center of dilation at the origin.
According to the exercise, the point C has these coordinates:
[tex]C(2,1)[/tex]
Therefore, in order to find the coordinates of C', you need to multiiply the coordinates of the point C by the scale factor 2.
Then, you get that the coordinates of the point C' are:
[tex]C'=(2*2,1*2)\\\\C'=(4,2)[/tex]
The correct answer is (1, one-half).
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the enlargement or reduction in the size of an image. If a point A(x, y) is dilated by a factor k, the new point is A'(kx, ky).
Given triangle ABC has vertices at A(1, 1), B(1.5, 3), C(2, 1). If the triangle is dilated by a scale factor of 2, the new point is:
A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2).
Hence the coordinates of C' is (1, one-half).
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