Question

Rectangle ABCD  has coordinates A(−10, 5) , B(10, 5), C(10, 0) , and  D(−10, 0) .   Rectangle A'B'C'D' has coordinates  A ′ (−10,−5), B ′ (10,−5) , C'(10, 0) , and D ′ (−10, 0) .   Rectangle A"B"C"D" has coordinates A ′′ (−2, −1),  B ′′ (2, −1) , C"(2, 0) , and D ′′ (−2, 0) . Which transformations describe why rectangles ABCD and   A"B"C"D" are similar? ​ Rectangle ABCD ​ was reflected across the y-axis and then dilated by a scale factor of 5 to form ​ Rectangle A"B"C"D" ​ ​ Rectangle ABCD ​ was reflected across the x-axis and then dilated by a scale factor of  1 5  to form Rectangle A"B"C"D" . ​ Rectangle ABCD ​ was dilated by a scale factor of  1 5  and then rotated 90° counterclockwise to form  ​ Rectangle A"B"C"D" ​ ​ Rectangle ABCD ​ was dilated by a scale factor of 5 and then rotated 90° counterclockwise to form ​ Rectangle A"B"C"D" ​ .

Answer 1

uh to anyone taking the 4.14 sequences of transformation on k12 (lol we're all cheating) its Rectangle ABCD ​ was reflected across the x-axis and then dilated by a scale factor of 1/5 to form Rectangle A"B"C"D"
i can confirm cuz i i took the quiz!

Answer 2

The correct transformation that is applied to Rectangle ABCD to get Rectangle A"B"C"D" is:

​ Rectangle ABCD ​ was reflected across the x-axis and then dilated by a scale factor of 1 5 to form Rectangle A"B"C"D" . ​

Explanation:

We are given vertices of rectangle ABCD as:

A(−10, 5) , B(10, 5), C(10, 0) , and D(−10, 0) .

Now we reflect the rectangle across the x-axis to get rectangle A'B'C'D' since the rule that is applied to this reflection is:

(x,y) → (x,-y)

Hence,

A(-10,5) → A'(-10,-5)

B(10,5) → B'(10,-5)

C(10,0) → C'(10,0)

D(-10,0) → D'(-10,0)

Now this rectangle A'B'C'D' is dilated by a scale factor of 1/5 to obtain rectangle A"B"C"D" ; Since the rule that is applied to this dilation is:

(x,y) → (x/5,y/5)

Hence, we have:

A'(-10,-5) → A"(-2,-1)

B'(10,-5) → B"(2,-1)

C'(10,0) → C"(2,0)

D'(-10,0) → D"(-2,0)