Triangle ABC is dilated by a scale factor of 2 with a center of dilation at the origin. What are the coordinates of the image of point C prime?

On a coordinate plane, triangle A B C has points (1, 1), (1.5, 3), (2, 1).
(2, 4)
(4, 2)
(One-half, 1)
(1, one-half)

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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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:

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: