Question

Describe the relationship between the point D(4, 6) and the point D'(10, 15) in terms of dilations. A) (x,y) → (x/2, y/2) B) (x,y) → (x/3, y/3) C) (x,y) → (x2, y2) D) (x,y) → (x3, y3)

Answer 1

The relationship between the points D(4, 6) and D'(10, 15) can be described in terms of dilations as (x, y) → (x/2, y/2). This indicates that the points have undergone a dilation where both the x and y coordinates are halved.

Step-by-step explanation:

Dilations are transformations that change the size of a figure but not its shape. In this case, the correct option is (x, y) → (x/2, y/2), which represents a dilation by a scale factor of 1/2 in both the x and y directions. This means that each coordinate of the original point D(4, 6) is multiplied by 1/2 to obtain the new coordinates of D'(10, 15).

The other options, such as (x/3, y/3), (x², y²), and (x³, y³), do not accurately represent the dilation observed between the points D and D'. The scale factor of 1/2 indicates a reduction in size, and the correct option reflects this by halving both the x and y coordinates.

In summary, the correct description of the relationship between D(4, 6) and D'(10, 15) in terms of dilations is (x, y) → (x/2, y/2).