What are the coordinates of the image of parallelogram ABCD after a dilation with center (0, 0) and a scale factor of 3? What are the coordinates of the image of parallelogram ABCD after a dilation with center (0, 0) and a scale factor of 1/2?

To find the coordinates of the image of parallelogram ABCD after dilation, we apply the dilation transformation to each vertex of the parallelogram.

Dilation with center (0, 0) and scale factor 3:

If the coordinates of the vertices of parallelogram ABCD are A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), and D(x₄, y₄), then the coordinates of the image after dilation are:

– A’ = (3 * x₁, 3 * y₁)

– B’ = (3 * x₂, 3 * y₂)

– C’ = (3 * x₃, 3 * y₃)

– D’ = (3 * x₄, 3 * y₄)

Dilation with center (0, 0) and scale factor 1/2:

Using the same coordinates for the vertices:

– A’ = (0.5 * x₁, 0.5 * y₁)

– B’ = (0.5 * x₂, 0.5 * y₂)

– C’ = (0.5 * x₃, 0.5 * y₃)

– D’ = (0.5 * x₄, 0.5 * y₄)

This means each coordinate is multiplied by the scale factor