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 the translation rule

Let the original vertex be \((x_1,y_1)\) and its image be \((x_2,y_2)\). The translation rule is \((x,y)\to(x+(x_2 - x_1),y+(y_2 - y_1))\).

Step2: Apply the translation rule to all vertices

Take each vertex \((x,y)\) of the triangle and use the rule from Step 1. For a vertex \((a,b)\) of the triangle, its image after translation is \((a+(x_2 - x_1),b+(y_2 - y_1))\).

Answer:

First, find the translation rule by subtracting the coordinates of the original vertex from the coordinates of its image. Then, apply this rule to all vertices of the triangle.