Geometry and two multiple choice questions

Question

Select the correct answer from each drop-down menu.
∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17).
∆XYZ has vertices at X(-10, 5), Y(-12, -2), and Z(-4, 15).
∆MNO has vertices at M(-9, -4), N(-3, -4), and O(-3, -15).
∆JKL has vertices at J(17, -2), K(12, -2), and L(12, 7).
∆PQR has vertices at P(12, 3), Q(12, -2), and R(3, -2).

1)Pick one to go with the sentence.
a/ Triangle ABC and Triangle XYZ
b/ Triangle ABC and Triangle MNO
c/ Triangle JKL and Triangle ABC
d/ Triangle PQR and Triangle XYZ

?can be shown to be congruent by a sequence of reflections and translations.

2)Pick one to go with the sentence.
a/ Triangle ABC and Triangle XYZ
b/ Triangle PQR and Triangle XYZ
c/ Triangle JKL and Triangle PQR
d/ Triangle JKL and Triangle XYZ

?can be shown to be congruent by a single rotation.

Answer 1

Problem #1 answer is B.

Triangles ABC and MNO are congruent 

  with lengths 6,11, and square-root(157).

A sequence of translations and reflections are needed

to flip the triangle from quadrant I to quadrant 3

 

Problem #2 answer is C

Triangles JKL and PQR are congruent

with lengths 5,9, and square-root(106).

A single rotation , looks like counter-clockwise 90 degrees

is needed to map JKL to PQR