Question

1) After a dilation, (-60, 15) is the image of (-12, 3). What are the coordinates of the image of (-2,-7) after the same dilation?
a) k = 5; (-10, -35)
b) k = 5; (-7, -2)
c) k = 1/5; (-2/5,-7/5)
d) k = 1/5; (-5/2,-5/7)

Answer 1

Answer:

a) k = 5; (-10, -35)

Step-by-step explanation:

Given:

Co-ordinates:

Pre-Image = (-12,3)

After dilation

Image = (-60,15)

The dilation about the origin can be given as :

Pre-Image$(x,y)\rightarrow Image(kx,ky)$

where $k$ represents the scalar factor.

We can find value of $k$ for the given co-ordinates by finding the ratio of $x$ or $y$ co-ordinates of the image and pre-image.

$k=\frac{Image}{Pre-Image}$

For the given co-ordinates.

Pre-Image = (-12,3)

Image = (-60,15)

The value of $k=\frac{-60}{-12}=5$

or $k=\frac{15}{3}=5$

As we get $k=5$ for both ratios i.e of $x$ and  $y$ co-ordinates, so we can say the image has been dilated by a factor of 5 about the origin.

To find the image of (-2,-7), after same dilation, we will multiply the co-ordinates with the scalar factor.

Pre-Image$(-2,-7)\rightarrow$ Image$((-2\times5),(-7\times 5))$

Pre-Image$(-2,-7)\rightarrow$ Image$(-10,-35)$ (Answer)