Question

Triangle ABC has vertices at A(3, 8) , B(11, 8) , and C(7, 12) .

Triangle FGH has vertices at F(8, 4) , G(16, 4) , and H(12, 8) .

Which sequence of transformations shows that triangle ABC and triangle FGH are congruent?

Select each correct answer.



Translate ​ triangle ABC ​ down 4 units then translate ​ triangle ABC ​ left 5 units.

Translate ​ triangle ABC ​ down 4 units then translate ​ triangle ABC ​ right 5 units.

Translate ​ triangle FGH ​ up 4 units then translate ​ triangle FGH ​ left 5 units. ​

Translate ​ triangle FGH ​ down 4 units then translate ​ triangle FGH ​ left 5 units. ​

Answer 1

These written below are the answers to these questions....

Translate triangle ABC down 5 units then left 2 units
Translate FGH up 5 units then right 2 units.

Answer 2

Option 2 and 3 are correct.

Explanation:

Triangle ABC has vertices at A(3, 8) , B(11, 8) , and C(7, 12) .

Triangle FGH has vertices at F(8, 4) , G(16, 4) , and H(12, 8) .

ΔABC ≅ ΔFGH

For congruence , Translation of all three coordinate must be same.

`A(3,8)\rightarrow F(8,4)`

Here x change 3 to 8 and y change 8 to 4

Point A shift 5 unit right and 4 unit down to get point F

`B(11,8)\rightarrow G(16,4)`

Here x change 11 to 16 and y change 8 to 4

Point B shift 5 unit right and 4 unit down to get point G

`C(7,12)\rightarrow H(12,8)`

Here x change 7 to 12 and y change 12 to 8

Point C shift 5 unit right and 4 unit down to get point H

In all three coordinate from ABC to FGH translation is same "5 unit right and 4 unit down"

True option: -

• Translate ​ triangle ABC ​ down 4 units then translate ​ triangle ABC ​ right 5 units.
• Translate ​ triangle FGH ​ up 4 units then translate ​ triangle FGH ​ left 5 units.