Question

Hallie applied a dilation given by the rule D 0.8(x,y)=(0.8x,0.8y )D0.8(x,y)=(0.8x,0.8y) and centered at the origin (0, 0) to a quadrilateral in a coordinate plane. The quadrilateral's image has vertices with coordinates of A′A′(-8, 12), B′B′(4, -8), C′C′(12, -4), and D′D′(16, 8). What are the coordinates of the image of point A? 1) (-6.4, 9.6) 2) (-8, 12) 3) (-10.4, 10.4) 4) (6.4, -9.6)

Answer 1

The coordinates of the image of point A, after applying the dilation
`(D_(0.8)(x, y) = (0.8x, 0.8y))` centered at the origin, are (-6.4, 9.6) thus option 1 is correct.

Step-by-step explanation:

To find the coordinates of the image of point A (denoted as A'), we apply the dilation to the original coordinates of A. Point A has coordinates (-8, 12). Using the dilation rule
`\(D_(0.8)(x, y) = (0.8x, 0.8y)\),`we multiply each coordinate by 0.8.

For point A:

`\[A' = D_(0.8)(-8, 12) = (0.8 * (-8), 0.8 * 12) = (-6.4, 9.6)\]`

Therefore, the correct answer is (-6.4, 9.6).

In summary, applying the dilation to point A involves multiplying its x and y coordinates by 0.8. This results in the image point A' with coordinates (-6.4, 9.6), option 1 is correct.

Answer 2

The correct option is 1)
`\((-6.4, 9.6)\)`.

To find the image of point A after applying the dilation, you can use the given dilation rule
`\( D_(0.8)(x, y) = (0.8x, 0.8y) \)`.

The coordinates of point A are (-8, 12). Applying the dilation:

`\[ D_(0.8)(-8, 12) = (0.8(-8), 0.8(12)) \]`

`\[ = (-6.4, 9.6) \]`

The image of point A after the dilation is
`\((-6.4, 9.6)\)`.