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

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin, the rule is \((x,y)\to(-x,-y)\).

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

Substitute \(x = 2\) and \(y=2\) into \((-x,-y)\). We get \((-2,-2)\) for \(L'\).

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

Substitute \(x = 4\) and \(y = 4\) into \((-x,-y)\). We get \((-4,-4)\) for \(M'\) (so the option \((-4,4)\) is wrong).

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

Substitute \(x=1\) and \(y = 6\) into \((-x,-y)\). We get \((-1,-6)\) for \(N'\) (so the option \((6,-1)\) is wrong).

Answer:

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