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 the rotation rule

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

Step2: Apply the rule to point \(L(2,2)\)

For \(L(2,2)\), using the rule \((x,y)\to(-x, -y)\), we get \(L'(- 2,-2)\).

Step3: Apply the rule to point \(M(4,4)\)

For \(M(4,4)\), using the rule \((x,y)\to(-x, -y)\), we get \(M'(-4,-4)\).

Step4: Apply the rule to point \(N(1,6)\)

For \(N(1,6)\), using the rule \((x,y)\to(-x, -y)\), we get \(N'(-1,-6)\).

Answer:

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

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