Question

Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure.Question options:A) (x, y) → (x – 4, y – 5)B) (x, y) → (x + 4, y + 5)C) (x, y) → (x + 5, y – 4)D) (x, y) → (x – 4, y + 5)

Answer 1

The triangle ΔABC is transformed into the triangle ΔA′B′C′.

As you can see from the graph, a horizontal shift to the left and a vertical shift upward are applied.

The coordinates of point A is (2, -2) and the coordinates of point A' is (-2, 3)

This means that the horizontal shift to the left is -4

$\begin{gathered} 2+x=-2 \\ x=-2-2 \\ x=-4 \end{gathered}$

The vertical shift upward is 5

$\begin{gathered} -2+y=3 \\ y=3+2 \\ y=5 \end{gathered}$

Therefore, the transformation is

$(x,y)\rightarrow(x-4,y+5)$

Option D is the correct answer.