The set of ordered pairs that represents the vertices of a triangle congruent to triangle ABC is A. (5, 5), (8, 0), (3, 4).Therefore, A. (5, 5), (8, 0), (3, 4) is correct .
Here's why:
Triangle ABC is shown in the coordinate plane.
We are asked to find a set of ordered pairs that represents the vertices of a triangle congruent to triangle ABC.
Congruent triangles have the same size and shape, but they can be in different locations or orientations.
In order to find a congruent triangle, we can try moving and/or rotating triangle ABC.
Set A, (5, 5), (8, 0), (3, 4), is the result of moving triangle ABC two units to the right.
This preserves the size and shape of the triangle, making it congruent to the original.
The other answer choices are not congruent to triangle ABC for the following reasons:
Set B, (5, 7), (4, 0), (-1, 0), is the result of moving triangle ABC two units up and one unit to the left.
This changes the orientation of the triangle, making it not congruent to the original.
Set C, (5, 5), (8, -4), (3, 0), is the result of moving triangle ABC four units down.
This changes the size of the triangle, making it not congruent to the original.
Set D, (3, 6), (6, -3), (2, 0), is a completely different triangle with different side lengths and angles.
It is not congruent to triangle ABC in any way.
Therefore, the only set of ordered pairs that represents the vertices of a triangle congruent to triangle ABC is A. (5, 5), (8, 0), (3, 4).