Troy drew a triangle with coordinates ( 5 , 6 ) , ( 5 , 4 ) , and ( 8 , 4 ) . He rotated the triangle 180° about the origin. What are the coordinates of the image? Select all that apply.
A. (−5, 6)
B. (−5, −4)
C. (−5, −6)
D. (−8, −4)
i hate doing this but i really dont know the answer and im already failing :( please help

When you rotate an image 180° about the origin, you are flipping it twice. An easy rule is that an (x, y) pair becomes (-x, -y). Now just reverse the sign of the coordinates. Our rotated shape has the coordinates (-5, -6), (-5, -4), and (-8, -4).

Answer Link

JeanaShupp JeanaShupp · Answer 2 · 2019-09-24T07:06:34+02:00

Answer: C. (−5, −6) D. (−8, −4)

Step-by-step explanation:

We know that the rule for rotation a shape by [tex]180^{\circ}[/tex] (counterclockwise or clockwise) is given by :-

[tex](x,y)\to(-x,-y)[/tex] [Polarity of coordinates gets changed]

Given : Troy drew a triangle with coordinates ( 5 , 6 ) , ( 5 , 4 ) , and ( 8 , 4 ) . He rotated the triangle 180° about the origin.

Then, the coordinates of the image will be :-

[tex]( 5 , 6 )\to(-5,-6)[/tex]

[tex]( 5 , 4 )\to(-5,-4)[/tex]

[tex]( 8 , 4 )\to(-8,-4)[/tex]

From the options, the coordinates of the image = (-5,-6) and (-8, -4)

Hence, option C and D are correct.