multiply the given coordinates by 4
2*4 = 8
-4*4 = -16
new cords are (8,-16)
Option: D is the correct answer.
The coordinates of the image of the point (2, –4) after a dilation with a center of (0, 0) and scale factor of 4 is:
(8,-16)
Dilation--
A dilation is a transformation which changes the shape of the original figure also known as the pre-image but the shape of the figure is retained.
The figure either shrinks or is expanded after applying this transformation depending on a parameter known as scale factor.
The dilation is done about a point which is known as a center of dilation.
If the dilation is done about the origin with a scale factor "k"
and if k>1 then the dilation will enlarge the original figure
and if k<1 then the dilation will reduce the size of the original figure.
Also, the change in coordinates of the pre-image is given by:
(x,y) → (kx,ky)
Here we have k=4
and (x,y)=(2,-4)
Hence, the coordinates of the image after dilation is:
(2×4,-4×4) i.e. (8,-16)
Hence, the coordinates of image is: (8,-16)
