If you translate trapezoid LMNP 3 units down and 8 units right, then you get trapezoid L'M'N'P'.
The coordinates of initial trapezoid are:
L(-7,0), M(-5,3), N(-1,3) and P(-1,0).
The coordinates of translated trapezoid trapezoid are:
L'(1,-3), M'(3,0), N'(7,0) and P'(7,-3).
1.
[tex] LL'=\sqrt{(-7-1)^2+(0+3)^2}=\sqrt{73} ,\\ PP'=\sqrt{(-1-7)^2+(0+3)^2}=\sqrt{73} ,\\ MM'=\sqrt{(-5-3)^2+(3-0)^2}=\sqrt{73} ,\\ NN'=\sqrt{(-1-7)^2+(3-0)^2}=\sqrt{73} [/tex].
This gives you conclusion that options A and B are correct and option D is incorrect.
2. Find vectors:
[tex] \vec{LL'}=(1+7,-3-0)=(8,-3),\\ \vec{MM'}=(3+5,0-3)=(8,-3),\\ \vec{NN'}=(7+1,0-3)=(8,-3),\\ \vec{PP'}=(7+1,-3-0)=(8,-3) [/tex].
All these vectors have the same coordinates, then they are parallel and all line segments that connect a point on the pre-image to its corresponding point on the image are parallel (choice E is correct).
Trapezoid LMNP is congruent to trapezoid L'M'N'P', because translation is isometric transformation (choice C is correct).
Answer: correct choices - A, B, C, E, incorrect choice - D.
