Question

1. 180° rotation

13a. which rotation about the origin results in (x,y)→( - x, - y)?
a. 180°
b. 90° ccw
c. 90° cw
d. reflection
13b. which is the image of (2, - 3) after 180° rotation?
a. ( - 2,3)
b. (3, - 2)
c. ( - 3,2)
d. (2,3)
13c. which is the image of ( - 4,5) after 180° rotation?
a. (4, - 5)
b. ( - 5,4)
c. (5, - 4)
d. ( - 4, - 5)
13d. which is the image of (0,7) after 180° rotation?
a. (0, - 7)
b. ( - 7,0)
c. (7,0)
d. (0,7)

Explanation:

Step1: Recall 180 - degree rotation rule

The rule for a 180 - degree rotation about the origin for a point \((x,y)\) is \((x,y)\to(-x,-y)\).

Step2: Solve 13a

For a 180 - degree rotation about the origin, if the point is \((x,y)\), the image is \((-x,-y)\). So the answer is A. 180°.

Step3: Solve 13b

Given the point \((2, - 3)\), applying the 180 - degree rotation rule \((x,y)\to(-x,-y)\), we get \((-2,3)\). So the answer is A. \((-2,3)\).

Step4: Solve 13c

Given the point \((-4,5)\), applying the 180 - degree rotation rule \((x,y)\to(-x,-y)\), we have \((4,-5)\). So the answer is A. \((4,-5)\).

Step5: Solve 13d

Given the point \((0,7)\), applying the 180 - degree rotation rule \((x,y)\to(-x,-y)\), we get \((0,-7)\). So the answer is A. \((0,-7)\).

Answer:

13a. A. 180°
13b. A. \((-2,3)\)
13c. A. \((4,-5)\)
13d. A. \((0,-7)\)