Question

What are the coordinates of the image of the point (2, –4) after a dilation with a center of (0, 0) and scale factor of 4? A. (0, 0) B. (2004-01-04-05-00_files/i0160000.jpg, –1) C. (2, –4) D. (8, –16)

Answer 1

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)

Explanation:

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)

Answer 2

multiply the given coordinates by 4

2*4 = 8

-4*4 = -16

new cords are (8,-16)