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_{180^{circ}}). which statements are true regarding the transformation? choose three correct answers. the coordinates of l are (-2,-2). the coordinates of m are (-4, 4). 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).

Explanation:

Step1: Identify transformation rule

The rule \(R_{180^{\circ}}\) for a rotation of \(180^{\circ}\) about the origin is \((x,y)\to(-x, -y)\).

Step2: Apply rule to point L

Given \(L(2,2)\), applying the rule \((x,y)\to(-x, -y)\) gives \(L'(- 2,-2)\).

Step3: Apply rule to point M

Given \(M(4,4)\), applying the rule \((x,y)\to(-x, -y)\) gives \(M'(-4,-4)\) (the second - given statement about \(M\) is wrong).

Step4: Apply rule to point N

Given \(N(1,6)\), applying the rule \((x,y)\to(-x, -y)\) gives \(N'(-1,-6)\).

Answer:

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