Question

Triangle ABC has vertices at A(4, 7) , B(13, 7) , and C(9, 11) .

Triangle FGH has vertices at F(1, 1) , G(10, 1) , and H(6, 5) .

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

Select each correct answer.



Translate ​ triangle FGH ​ up 6 units then translate ​ triangle FGH ​ right 3 units. ​

Translate ​ triangle ABC ​ up 6 units then translate ​ triangle ABC ​ right 3 units.

Translate ​ triangle FGH ​ down 6 units then translate ​ triangle FGH ​ left 3 units. ​

Translate ​ triangle ABC ​ down 6 units then translate ​ triangle ABC ​ left 3 units.

Answer 1

The answer is D Do you want an explanation?

Answer 2

Option D is right

Explanation:

Given that

Triangle ABC has vertices at A(4, 7) , B(13, 7) , and C(9, 11) .

Triangle FGH has vertices at F(1, 1) , G(10, 1) , and H(6, 5) .

FGH is obtained by a set of transformations of ABC

Compare the coordinates of ABC with FGH in the same order

We find a pattern.

X coordinates of vertices of ABC reduced by 3 and y coordinates reduced by 6.

This implies there is a vertical shift down by 6 units and horizontal shift 3 to left for ABC to get FGH

Translate ​ triangle ABC ​ down 6 units then translate ​ triangle ABC ​ left 3 units.

is the correct answer.