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 FDE is dilated to create smaller triangle F prime D prime E prime. Triangle FDE has points (- 9, 3), (- 9, 9), (- 6, 6). Triangle F prime D prime E prime has points (- 3, 1), (- 3, 3), and (- 2, 2). Which statements are true?A. ∠F corresponds to ∠F'. B. Segment EE' is parallel to segment FF'. C. The distance from point D' to the origin is One-third the distance of point D to the origin. D. The measure of ∠E' is One-third the measure of ∠E. E. △DEF △D'E'F'.

Answer 1

Answer:

a) True.

b) False.

c) True.

d) False.

e) True.

Step-by-step explanation:

A. ∠F corresponds to ∠F'.  True.

B. Segment EE' is parallel to segment FF'.  False. They intersect each other at the origin.

C. The distance from point D' to the origin is One-third the distance of point D to the origin.   True.

We can get the ratio D'E'/DE:

$D'E'=\sqrt{(-3-0)^{2} +(-3-0)^{2} } =\sqrt{18}=3\sqrt{2} \\ DE=\sqrt{(-9-0)^{2} +(-9-0)^{2} } =\sqrt{162}=9\sqrt{2}\\ \frac{D'E'}{DE} =\frac{3\sqrt{2}}{9\sqrt{2}} =\frac{1}{3} \\ D'E'=\frac{1}{3}*DE$

D. The measure of ∠E' is One-third the measure of ∠E. False.

E. △DEF ~ △D'E'F'. True. They are similar triangles.

Answer 2

A. ∠F corresponds to ∠F' : True.

B. Segment EE' is parallel to segment FF' : False.

C. The distance from point D' to the origin is One-third the distance of point D to the origin. : True.

D. The measure of ∠E' is One-third the measure of ∠E : False.

E. △DEF ~ △D'E'F' : True.

As 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'.

The center of dilation = (0, 0)

And Triangle FDE has points: (- 9, 3), (- 9, 9), (- 6, 6).

Triangle F'D'E' has points : (- 3, 1), (- 3, 3), (- 2, 2)

So,

A. ∠F corresponds to ∠F'. ( True)

B. Segment EE' is parallel to segment FF'. (False)

As they intersect each other at the origin.

C. The distance from point D' to the origin is One-third the distance of point D to the origin.    ( True)

Now, let us find the ratio D'E'/DE:

Length DE

$=\sqrt{(-9-0)^{2}+ (-9-0)^{2}} \\=9\sqrt{2}$

And length D'E'

$=\sqrt{(-3-0)^{2}+ (-3-0)^{2}} \\=3\sqrt{2}$

Ratio D'E'/DE

$=\frac{3\sqrt{2} }{9\sqrt{2} } \\=\frac{1}{3}$

D. The measure of ∠E' is One-third the measure of ∠E. ( False)

E. △DEF ~ △D'E'F'.  ( True)

As they are similar triangles.

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