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## how can i determine the translation of a figure given only a figure?

The question ask to determine the translation of a triangle. And they only give me the location of three points
(3,6)
(6,-3)
(-2,-3)

Can i find the translation giving only that imformation?
You have been asked by the police department to find three locations the Acute Perps gang is likely to hit in the coming weeks. Because the gang sticks to a triangular pattern, the locations could be a translation, reflection, or rotation of the original triangle. For this step, identify and label three points on the coordinate plane that are a translation of the original triangle. Next, use the coordinates of your translation along with the distance formula to show that the two triangles are congruent by the SSS postulate. You must show all work with the distance

Do you think that this is just asking me to choose any point i want and then use that to do my next step?
yes i think it means choose your own point

The goal is to translate the triangle with the given vertices in any which you choose and then prove that the original triangle and the translated triangle are congruent by the side-side-side postulate (i.e., if 3 sides of a triangle are equal to 3 sides of another triangle (in length/distance) then the 2 triangles are congruent).

For example, let's say you want to translate the given triangle 4 units to the right and 2 units down. Then you add 4 units to the x-coordinate of each vertex and subtract 2 units from the y-coordinate of each vertex to obtain the this translation. That is,

(3, 6)    --> (3+4, 6-2)=(7, 4)
(6, -3)   --> (6+4, -3-2)=(10, -5)
(-2, -3)  --> (-2+4, -3-2)=(2, -5)

Now compute the length of each side of both triangles using the distance formula. If the lengths of the 3 sides of the original triangle are equal to the length of the 3 sides of the translated triangle, then they are congruent by the SSS postulate.
"identify and label three points on the coordinate plane that are a translation of the original triangle", where the original triangle has the points you gave as its vertices.

So just make up a translation, <h,k>, and translate all three points, (x,y) ––> (x+h,y+k).

"Next, use the coordinates of your translation along with the distance formula to show that the two triangles are congruent by the SSS postulate."

Straightforward algebra.