Question

use the graph and the translation (t(x,y)=(x + 3,y+4)) to answer parts a and b below.

a. (type ordered - pairs.)
b. graph the pre - image and image of (\triangle abc). choose the correct graph below.

Explanation:

Step1: Identify the translation rule

The translation is $(x,y)\to(x + 5,y+4)$. This means we add 5 to the x - coordinate and 4 to the y - coordinate of each vertex of $\triangle ABC$.

Step2: Assume vertex coordinates

Let's assume the coordinates of the vertices of $\triangle ABC$ are $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$. The new coordinates of the vertices of the image will be $A'(x_1 + 5,y_1+4)$, $B'(x_2 + 5,y_2+4)$, $C'(x_3 + 5,y_3+4)$.

Step3: Analyze the graph

We need to look for the graph where the original triangle $\triangle ABC$ (black - colored) and its translated image (blue - colored) follow the rule of moving 5 units to the right (increase in x - value) and 4 units up (increase in y - value).

Answer:

(Without seeing the actual coordinates of the vertices and fully analyzing the options, we can't give a specific letter - choice answer. But the correct graph will have the blue - colored triangle (image) 5 units to the right and 4 units up from the black - colored triangle (pre - image).)