+0

# I need clarification- similarity ​

0
74
2 For question 1, the answer needed is the coordinate of F' and question 2, the coordinate of L'.

The answers I got from working the problems out were (20/3, 28/3) and (-3, 1/2) respectively but upon graphing these answers, I don't feel like it's right. For both questions, the center of the figure is (4, -2).

For question 1, I need to give the leftmost point and question two the bottom most point. I got the answers (9/4, -3) and (7/4, -2) respectively.

Could someone verify these answers for me? Thank you in advance!

Jan 7, 2021

### 2+0 Answers

#1
+1

(1)    E = (0,0)   F(1,5)    G(7,2)    center of dilation =  (5,2)   scale factor  = 2

Dilation rule   is

Reverse the signs on the  coordinates of the  center =  ( -5 , -2)

The "new " coordinates  are  ( x - 5, y - 2)

Apply the scale factor  =  (2x - 10, 2y - 4)

Add  back the center coordinates  = ( 5, 2)

[ (2x - 10 + 5). ( 2y - 4 + 2) ] =

( 2x  - 5   ,  2y   - 2)

E' = [ (2(0) - 5, 2(0)-2)  ]  = (-5, -2  )

F'  =   [ ( 2(1)  - 5 , 2(5) -2)  ] =  ( -3, 8)

G' =    [ 2(7)  -  5, 2(2) - 2 ] =  ( 9, 2)

See here  :    Jan 7, 2021
edited by CPhill  Jan 7, 2021
#2
+1

2.  Similar to  1

Reverse the coordinates of the  center   = (3,-3)

The "new" coordinates   =  [(x  + 3 , (y - 3)  ]

Apply the scale factor   = ( (1/3)x + 1, (1/3)y - 1)

Add  back  the coordinates of the center

[ (1/3)x + 1 - 3  ,  (1/3)y  - 1 +3 ]  =

[ x/3 - 2 , y/3 - 2 ]    =dilation rule

You should be able to finish this one  by applying the dilation rule to  L,M,N,P

Also....find the  coordinates of the parallelogram  at the bottom and use the  same proceedure to find the  dilation rule  for the  first one

For the second one....just apply the scale factor to  the  computed  points  you got  in  1   Jan 7, 2021
edited by CPhill  Jan 7, 2021
edited by CPhill  Jan 7, 2021