Question

a triangle has vertices at l(2, 2), m(4, 4), and n(1, 6). the triangle is transformed according to the rule ( r_{0, 180^circ} ). which statements are true regarding the transformation? choose three correct answers. the coordinates of n are (6, -1). the rule for the transformation is ( (x, y) \to (-x, -y) ). the coordinates of n are (-1, -6). the coordinates of l are (-2, -2). the coordinates of m are (-4, 4).

Explanation:

Step1: 180° rotation rule

A 180° rotation about the origin transforms (x,y) to (-x,-y).

Step2: Calculate L'

Original L(2,2): (-2,-2). So L'(-2,-2) is correct.

Step3: Calculate M'

Original M(4,4): (-4,-4). M'(-4,4) is wrong.

Step4: Calculate N'

Original N(1,6): (-1,-6). So N'(-1,-6) is correct.

Step5: Verify transformation rule

Rule (x,y)→(-x,-y) matches 180° rotation.

Answer:

The rule for the transformation is (x,y)→(-x,-y), The coordinates of L' are (-2,-2), The coordinates of N' are (-1,-6)