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

Determine the change in x - and y - coordinates between the original vertex and its image. Let the original vertex be \((x_1,y_1)\) and its image 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 remaining 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 \(x_3'=x_3+(x_2 - x_1)\) and \(y_3'=y_3+(y_2 - y_1)\), and \(x_4'=x_4+(x_2 - x_1)\) and \(y_4'=y_4+(y_2 - y_1)\).

Answer:

Find the translation vector from the given vertex - image pair and apply it to the other two vertices of the triangle.