Question

Rectangle ABCD is translated (x + 2, y − 3) and then rotated 180° about the origin. Complete the table to show the locations of A″, B″, C″, and D″ after both transformations.

Rectangle ABCD is shown. A is at negative 5, 1. B is at negative 5, 3. C is at negative 1, 3. D is at negative 1, 1.


A (− 5, 1) A″ ?
B (−5, 3) B″ ?
C (−1, 3) C″ ?
D (−1, 1) D″ ?
A) A″ (−2, −3), B″ (0, −3), C″ (0, 1), D″ (−2, 1)
B) A″ (−3, −2), B″ (−3, 0), C″ (1, 0), D″ (1, −2)
C) A″ (3, 0), B″ (3, 2), C″ (−1, 2), D″ (−1, 0)
D) A″ (3, 2), B″ (3, 0), C″ (−1, 0), D″ (−1, 2)

Answer 1

Answer: D) A″ (3, 2), B″ (3, 0), C″ (−1, 0), D″ (−1, 2)

Answer 2

D

Explanation:

Rectangle ABCD has vertices A(-5, 1), B(-5, 3), C(-1, 3), D(-1, 1).

1. Rectangle ABCD is translated with the rule

`(x,y)\rightarrow  (x + 2, y-3)`

Then

• 
  `A(-5,1)\rightarrow A'(-3,-2);`
• 
  `B(-5,3)\rightarrow B'(-3,0);`
• 
  `C(-1,3)\rightarrow C'(1,0);`
• 
  `D(-1,1)\rightarrow D'(1,-2).`

2. Rotation 180° about the origin has the rule

`(x,y)\rightarrow (-x,-y)`

Then

• 
  `A'(-3,-2)\rightarrow A''(3,2);`
• 
  `B'(-3,0)\rightarrow B''(3,0);`
• 
  `C'(1,0)\rightarrow C''(-1,0);`
• 
  `D'(1,-2)\rightarrow D''(-1,2).`