Question

AABC has vertices at A(12, 8), B(4,8), and C(4, 14).

Answer 1

Answer:

Triangle ABC and triangle MNO are congruent. A Rotation is a single rigid transformation that maps the two congruent triangles.

Step-by-step explanation:

ΔABC has vertices at A(12, 8), B(4,8), and C(4, 14).

• length of AB = √[(12-4)² + (8-8)²] = 8

• length of AC = √[(12-4)² + (8-14)²] = 10

• length of CB = √[(4-4)² + (8-14)²] = 6

ΔMNO has vertices at M(4, 16), N(4,8), and O(-2,8).

• length of MN = √[(4-4)² + (16-8)²] = 8

• length of MO = √[(4+2)² + (16-8)²] = 10

• length of NO = √[(4+2)² + (8-8)²] = 6

Therefore:

• AB ≅ MN

• AC ≅ MO

• CB ≅ NO

and ΔABC ≅ ΔMNO by SSS postulate.

In the picture attached, both triangles are shown. It can be seen that counterclockwise rotation of ΔABC around vertex B would map ΔABC into the ΔMNO.