Question

Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) is dilated using a scale factor of 3/4 to create polygon A′B′C′D′. Determine the vertices of polygon A′B′C′D′.

Answer 1

The vertices of the dilated polygon A'B'C'D', using a scale factor of 3/4, are A'(-3, 4.5), B'(-1.5, 1.5), C'(3, -1.5), and D'(3, 3). Each vertex of the original polygon is multiplied by the scale factor to get the coordinates of the new polygon.

Step-by-step explanation:

To determine the vertices of the dilated polygon A'B'C'D', we apply the scale factor of 3/4 to each of the coordinates of vertices A, B, C, and D of the original polygon ABCD. The dilation process involves multiplying each x- and y-coordinate by the scale factor. The formula to find the new coordinates is (x', y') = (scale factor × x, scale factor × y).

For vertex A(-4, 6), the calculation would be:

• A' = (3/4 × -4, 3/4 × 6) = (-3, 4.5)

Repeating this process for each vertex:

• B' = (3/4 × -2, 3/4 × 2) = (-1.5, 1.5)
• C' = (3/4 × 4, 3/4 × -2) = (3, -1.5)
• D' = (3/4 × 4, 3/4 × 4) = (3, 3)

So the vertices of polygon A'B'C'D' are A'(-3, 4.5), B'(-1.5, 1.5), C'(3, -1.5), and D'(3, 3).