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 a dilation with center (0, 0) and given scale factors, you can use the formula for dilation:

New Coordinates = (Scale Factor) × (Original Coordinates)

1. For a scale factor of 3:

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

– A’ = (3 * x₁, 3 * y₁)

– B’ = (3 * x₂, 3 * y₂)

– C’ = (3 * x₃, 3 * y₃)

– D’ = (3 * x₄, 3 * y₄)

2. For a scale factor of 1/2:

– Using the same original coordinates, the new coordinates after dilation would be:

– A’ = (1/2 * x₁, 1/2 * y₁)

– B’ = (1/2 * x₂, 1/2 * y₂)

– C’ = (1/2 * x₃, 1/2 * y₃)

– D’ = (1