Question

determine how to translate triangle abc to triangle abc. (x + 2, y - 5) (x - 2, y - 9) (x + 2, y - 9)

Explanation:

Step1: Recall translation rule

Translation in a coordinate - plane is given by $(x,y)\to(x + a,y + b)$, where $a$ is the horizontal displacement and $b$ is the vertical displacement.

Step2: Analyze horizontal displacement

If $a>0$, the figure moves right; if $a < 0$, the figure moves left. To move from $\triangle A'B'C'$ to $\triangle ABC$, we need to find the change in the $x$ - coordinates of corresponding points.

Step3: Analyze vertical displacement

If $b>0$, the figure moves up; if $b < 0$, the figure moves down. We find the change in the $y$ - coordinates of corresponding points.

Answer:

We need to know the coordinates of corresponding points of $\triangle A'B'C'$ and $\triangle ABC$ to determine the exact translation. But based on the given options, we would check the horizontal and vertical changes for each option. Without the actual coordinates of the triangles, we can't definitively choose from the given $(x + 2,y-5),(x - 2,y-9),(x + 2,y-9)$. If we assume we have calculated the horizontal and vertical displacements correctly by comparing corresponding vertices, we would select the option that matches those displacements. For example, if a vertex of $\triangle A'B'C'$ has coordinates $(x_1,y_1)$ and the corresponding vertex of $\triangle ABC$ has coordinates $(x_2,y_2)$ such that $x_2=x_1 + 2$ and $y_2=y_1-9$, the translation is $(x + 2,y-9)$.