Question

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 original triangle with coordinates \((x_0,y_0)\), find the new coordinates \((x,y)\) by adding the components of the translation vector. So \(x=x_0+(x_2 - x_1)\) and \(y=y_0+(y_2 - y_1)\).

Answer:

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