Question

explaining how to translate a figure
you are given the coordinates of a triangle and coordinates for only one of the vertices of its image under a translation. explain how to translate the entire triangle.

Explanation:

Step1: Find translation vector

Subtract the original vertex coordinates from the translated - vertex coordinates. Let the original vertex be $(x_1,y_1)$ and the translated vertex be $(x_2,y_2)$. The translation vector $\vec{v}=(x_2 - x_1,y_2 - y_1)$.

Step2: Translate other vertices

For each of the other two vertices of the triangle with coordinates $(x_3,y_3)$ and $(x_4,y_4)$, find their new coordinates $(x_3',y_3')$ and $(x_4',y_4')$ by adding the components of the translation vector. So, $(x_3',y_3')=(x_3+(x_2 - x_1),y_3+(y_2 - y_1))$ and $(x_4',y_4')=(x_4+(x_2 - x_1),y_4+(y_2 - y_1))$.

Answer:

First, find the translation vector by subtracting the original - vertex coordinates from the translated - vertex coordinates. Then, add the components of this translation vector to the coordinates of the other two vertices of the triangle to get the coordinates of the translated triangle.