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0273hdj
16.12.2019 •
Mathematics
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)
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Ответ:
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)](/tpl/images/0420/7889/ac714.png)
where
represents the scalar factor.
We can find value of
for the given co-ordinates by finding the ratio of
or
co-ordinates of the image and pre-image.
For the given co-ordinates.
Pre-Image = (-12,3)
Image = (-60,15)
The value of![k=\frac{-60}{-12}=5](/tpl/images/0420/7889/b73cb.png)
or![k=\frac{15}{3}=5](/tpl/images/0420/7889/07162.png)
As we get
for both ratios i.e of
and
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
Image![((-2\times5),(-7\times 5))](/tpl/images/0420/7889/179f1.png)
Pre-Image
Image
(Answer)
Ответ:
you should try a bar graph!!!