A dilation has center​ (0,0). Find the image of the point ​L(​-6,0​) for the scale factor 4 .

Question

D4(L)=L′

​(Type an ordered pair. Simplify your​ answer.)

Answer 1

For a dilation about the origin (0,0) with scale factor k. the rule is:

dilate by k

(x,y) -------------> (kx, ky)

In your case, (x,y) = (-6,0) and k = 4.

Answer 2

So the image that we are dilating is merely a point, point L, located at (-6, 0).

The dilation is centered at the origin (0,0) and we are dilating this image by a scale factor of 6.

So, you will simply take your X-VALUE and multiply it by 6, then take your Y-VALUE and multiply it by 6

We are starting at point L: (-6, 0) and dilating it at a scale factor of 6, so (-6x6, 0x6) = (-36, 0)

L' = (-36, 0)

Note: If we were dilating it by a scale factor of 1/6 instead of 6, then you would:

L = (-6, 0)

L' = [-6•(1/6), 0•(1/6)] = (-1, 0)