Triangle lies in the first quadrant. Points and are reflected across the line to points and , respectively. Assume that none of the vertices of the triangle lie on the line . Which of the following statements is always true?
The centroid of triangle is the reflection of the centroid of triangle across .
The perimeter of triangle is equal to the perimeter of triangle .
The line segment connecting to is perpendicular to the line .
The orientation of triangle is opposite to the orientation of triangle .
Lines and are parallel to each other.