Polygon ABCD has vertices A(–4, 0), B(–2, 4), C(3, 4), and D(8, 0). Polygon A'B'C'D' is the dilation image of ABCD, using the center (0, 0) and a scale factor of 0.5. What are the coordinates of A', B', C', and D'?

This question has me confused. Could someone just show me an example way I would solve it and I'll plug in the numbers myself? Thanks

Sure! To find the coordinates of the vertices A', B', C', and D' of the dilated polygon A'B'C'D', we can use the formula for dilation:

(x', y') = (k * x, k * y)

Here, (x, y) represents the coordinates of the original vertices of ABCD, (x', y') represents the coordinates of the dilated vertices A'B'C'D', and k represents the scale factor.

Let's plug in the values from the question:

Original polygon ABCD:
A(-4, 0), B(-2, 4), C(3, 4), D(8, 0)

Scale factor: k = 0.5
Center of dilation: (0, 0)

Now, let's calculate the coordinates of each vertex of the dilated polygon:

Vertex A':
(x', y') = (k * x, k * y) = (0.5 * -4, 0.5 * 0) = (-2, 0)
So, A' has coordinates (-2, 0).

Vertex B':
(x', y') = (k * x, k * y) = (0.5 * -2, 0.5 * 4) = (-1, 2)
So, B' has coordinates (-1, 2).

Vertex C':
(x', y') = (k * x, k * y) = (0.5 * 3, 0.5 * 4) = (1.5, 2)
So, C' has coordinates (1.5, 2).

Vertex D':
(x', y') = (k * x, k * y) = (0.5 * 8, 0.5 * 0) = (4, 0)
So, D' has coordinates (4, 0).

Therefore, the coordinates of the dilated polygon A'B'C'D' are:
A'(-2, 0), B'(-1, 2), C'(1.5, 2), D'(4, 0).

I hope this explanation clarifies how to solve this type of problem! Let me know if you have any other questions.