Question

Triangle DEF was dilated according to the rule DO,One-third(x,y)(one-third x, one-third y) to create similar triangle D'E'F'. On a coordinate plane, (0, 0) is the center of dilation. Triangle F D E is dilated to create smaller triangle F prime D prime E prime. Triangle F D E has points (negative 9, 3), (negative 9, 9), (negative 6, 6). Triangle F prime D prime E prime has points (negative 3, 1), (negative 3, 3), and (negative 2, 2). Which statements are true? Select three options. ∠F corresponds to ∠F'. Segment EE' is parallel to segment FF'. The distance from point D' to the origin is One-third the distance of point D to the origin. The measure of ∠E' is One-third the measure of ∠E. △DEF △D'E'F'

Answer 1

Given :  Triangle DEF was dilated  to triangle D'E'F'  one third x & one third y , origin being center of Dilation .  F  ( - 9 , 3)  , D  ( - 9 , 9)   E  (-6 , 6)  F' ( -3  , 1)   , D' ( -3 , 3)  , E' ( -2 , 2)

To find : choose all correct options

Solution:

F  ( - 9 , 3)  , D  ( - 9 , 9)   E  (-6 , 6)

F' ( -3  , 1)   , D' ( -3 , 3)  , E' ( -2 , 2)

DE = 3√2    EF  = 3√2    DF   = 6

D'E' = √2    E'F'  ='√2    D'F'   = 2

DE/D'E'   =  EF/E'F'   =  DF/D'F'  = 3

Hence triangle △DEF ≈ △D'E'F'

△DEF ≈ △D'E'F'   - TRUE

as Triangle are similar

∠F corresponds to ∠F'    - TRUE

EE'   Slope  = ( 6 - 2)/( - 6 + 2)  = 4/(-4) = -1

FF'  Slope =  (3 - 1)/(-9 + 3)  = 2/(-6)  = -1/3

Slope is not same

Hence Segment EE' is not parallel to segment FF'

distance of point D  from origin = √9² + 9² = 9√2

distance of point D'  from origin = √3² + 3² = 3√2

3√2 / 9√2   = 1/3

The distance from point D' to the origin is One-third the distance of point D to the origin  - TRUE

The measure of ∠E' is One-third the measure of ∠E  ( not true)

as  ∠E' =  ∠E

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Answer 2

Answer:

the answer is 3/10. which is C. got it right edu2020.

Step-by-step explanation:

Point O is the center of dilation. Triangle D E F is dilated to create smaller triangle D prime E prime F prime. The length of O F prime is 3. The length of F prime F is 7.

What is the scale factor of the dilation of triangle DEF?

Three-tenths

Three-sevenths

Seven-thirds

7