Question

A triangle has vertices T(3, 7), U(6, -6), and V(5, -9).

The image of the triangle has vertices T'(8, 1), U'(-5,
4), and V'(-8, 3).
Which transformations could have produced the
image?
OT(1.-2) ° Ty=x
Ory=x0 T(1, -2)
O Ta. -2) o Ro, 180°
O
O Ro. 180
Ta. -2)

Answer 1

The image of the triangle can be produced by a combination of a translation and a reflection transformation.

Step-by-step explanation:

The image of the triangle can be produced by a combination of a translation and a reflection transformation. Let's break it down step by step:

1. Translation: The triangle is translated by moving each vertex a certain distance to the right and up. The translation vector, represented by (x, y), can be found by subtracting the coordinates of the original vertex from the coordinates of the image vertex. In this case, (x, y) = (8 - 3, 1 - 7) = (5, -6).
2. Reflection: The triangle is reflected across the line y = x, which means that the x-coordinates and y-coordinates are swapped. The reflected vertex can be found by swapping the x-coordinate and y-coordinate of each vertex. In this case, the reflected triangle has vertices T'(-2, 5), U'(4, -5), and V'(9, -8).

Therefore, the transformations that could have produced the image are a translation of (5, -6) and a reflection across the line y = x.