Question

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

Answer 1

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
`(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 ((2)/(3)(x-1)+1, (2)/(3)(y+1)-1)`

or

`(x, y) \rightarrow ((2)/(3)x -(2)/(3)+1 , (2)/(3)y+(2)/(3)-1)`

or

`(x, y) \rightarrow ((2)/(3)x+(1)/(3) , (2)/(3)y-(1)/(3) )`

Now,

for R = (2,1)

the image R' =
`((2)/(3)(2)+(1)/(3) , (2)/(3)(1)-(1)/(3) )` or

`((4)/(3)+(1)/(3) , (2)/(3)-(1)/(3) )`

⇒ R' =
`((5)/(3) , (1)/(3))`

For S = (2, -2) ,

the image S'=
`((2)/(3)(2)+(1)/(3) , (2)/(3)(-2)-(1)/(3) )` or

`((4)/(3)+(1)/(3) , (-4)/(3)-(1)/(3) )`

⇒ S' =
`((5)/(3) , -(5)/(3))`

and For T = (-1, -2)

The image T' =
`((2)/(3)(-1)+(1)/(3) , (2)/(3)(-2)-(1)/(3) )` or

`((-2)/(3)+(1)/(3) , (-4)/(3)-(1)/(3) )`

⇒ T' =
`((-1)/(3) , (-5)/(3))`

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