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Delvig [45]
2 years ago
10

2. Draw the image of RST under the dilation with scale factor 2/3 and center of dilation (1,-1). Label the image RST .

Mathematics
1 answer:
professor190 [17]2 years ago
5 0

Answer:

From the graph: we have the coordinates of RST i.e,

R = (2,1) , S = (2,-2) , T = (-1,-2)

Also, it is given the scale factor \frac{2}{3} and center of dilation C (1,-1)

The mapping rule for the center of dilation applied for the triangle as shown below:

(x, y) \rightarrow (\frac{2}{3}(x-1)+1, \frac{2}{3}(y+1)-1)

or

(x, y) \rightarrow (\frac{2}{3}x -\frac{2}{3}+1 , \frac{2}{3}y+\frac{2}{3}-1)

or

(x, y) \rightarrow (\frac{2}{3}x+\frac{1}{3} , \frac{2}{3}y-\frac{1}{3} )

Now,  

for R = (2,1)  

the image R' = (\frac{2}{3}(2)+\frac{1}{3} , \frac{2}{3}(1)-\frac{1}{3} ) or

(\frac{4}{3}+\frac{1}{3} , \frac{2}{3}-\frac{1}{3} )

⇒ R' = (\frac{5}{3} , \frac{1}{3})  

For S = (2, -2) ,

the image S'=  (\frac{2}{3}(2)+\frac{1}{3} , \frac{2}{3}(-2)-\frac{1}{3} ) or

(\frac{4}{3}+\frac{1}{3} , \frac{-4}{3}-\frac{1}{3} )

⇒ S' = (\frac{5}{3} , -\frac{5}{3})

and For T = (-1, -2)

The image T' =  (\frac{2}{3}(-1)+\frac{1}{3} , \frac{2}{3}(-2)-\frac{1}{3} ) or

(\frac{-2}{3}+\frac{1}{3} , \frac{-4}{3}-\frac{1}{3} )

⇒ T' = (\frac{-1}{3} , \frac{-5}{3})

Now, label the image of RST on the graph as shown below in the attachment:

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