What degree of rotation will cause the triangle below to map onto itself ?

The triangle is rotated 360° ⇒ answer D

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

anti-clockwise around the origin

- If point (x , y) rotated about the origin by angle 360°

∴ Its image is (x , y)  the point itself

* There is no difference between rotating 360° clockwise or  

anti-clockwise around the origin

* Now lets solve the problem

∵ The vertices of the triangle ABC are:

  A is (-6 , 3) , B is (-5 , 7) , C is (-4 , 3)

∵ The triangle map onto itself

∴ A = A'

∴ B = B'

∴ C = C'

∴ The triangle is rotated 360° about the origin

x = -5

step-by-step explanation: