Question

The vertices of ΔABC are (-2,0), (-2, 3), and (-5, 1). T(x,y) = (x + 1, 3y) represents the transformation of the triangle. What are the coordinates of the vertices for ΔA'B'C'? Are the pre-image and image congruent? Justify your answer.

A) (0,-1),(9,1),(3,-4); The triangles are congruent because all transformations result in congruent figures.
B) (1,0),(1,9),(-4, 3); The triangles are not congruent because ΔA'B'C' is a reflection of ΔABC.
C) (-1,3),(-1,3),(-4,3); The triangles are congruent because the same transformation was performed on each vertex.
D) (-1,0),(-1,9),(-4,3); The triangles are not congruent because 3y is a dilation which increases the size of ΔA'B'C'.

Answer 1

The correct answer is D.
T(x, y) = (x + 1, 3y) is telling you what to do to each point.

Answer 2

choice D is the correct answer. the transformation (x+1) means add 1 to the original x coordinates, so they transform from -2, -2, -5, to -1,-1,-4
the transformation 3y means the original y coordinates multiply 3, so they transform from 0,3,1 to 0,9,3
the two triangles are not congruent because the x values shift upward but the y values are dilated. They would be congruent if both x and y are shifted in the same direction, or both x and y are dilated by the same factor.