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? select three options.
□ the rule for the transformation is ( (x, y) \to (-x, -y) ).
□ the coordinates of l are (-2,-2).
□ the coordinates of m are (-4,4).
□ the coordinates of n are (6,-1).
□ the coordinates of n are (-1,-6).

Explanation:

Step1: Recall 180° rotation rule

A 180° rotation about the origin (\(R_{0,180^\circ}\)) has the rule \((x,y)\to(-x,-y)\). So first option is checked.

Step2: Find \(L'\) coordinates

For \(L(2,2)\), apply \((x,y)\to(-x,-y)\): \(-2,-2\). So \(L'\) is \((-2,-2)\), second option is checked.

Step3: Find \(M'\) coordinates

For \(M(4,4)\), apply the rule: \(-4,-4\), not \((-4,4)\). So third option is wrong.

Step4: Find \(N'\) coordinates

For \(N(1,6)\), apply the rule: \(-1,-6\), not \((6,-1)\). So fourth option is wrong, fifth option is checked.

Answer:

The rule for the transformation is \((x,y)\to(-x,-y)\), The coordinates of \(L'\) are \((-2,-2)\), The coordinates of \(N'\) are \((-1,-6)\) (i.e., the first, second, and fifth options).