I am a triangle that has been translated to rest on (-1, -1),(-1,3), and (-2,1). Before translation I was on (2,1) and (2,5). Where is my third vertex before I was translated?
I noticed that (-1,-1) and (-1,3) had the same x's in the final position.
So in a translation , lines remain parallel, so notice that the 2 given points also have the same x's
Therefore (2,1) ---> (-1,-1)
and (2,5) ----> (-1,3)
looks like 3 was subtracted from the x, and
2 was subtracted from the y
so (? , ? -----> (-2,1)
must have been (1,3)
sketch each triangle, you will see that they are congruent.
i am a rhombus that rest on (1,2), (3,4), (1,6), (-1,4) after translation. if i was on (2,0), (0,2) and (-2,0) before being translated. where did my fourth corner rest.
To find the third vertex of the triangle before it was translated, we can use the concept of translation in geometry.
Translation involves moving an object from one location to another without changing its shape or orientation. In this case, the triangle has been translated by a certain amount to rest on the points (-1, -1), (-1, 3), and (-2, 1).
To find the third vertex before the translation, we need to reverse the translation process. This means moving the triangle back to its original position. The reverse translation involves moving the triangle by the same amount but in the opposite direction.
In this case, the translation involved moving the triangle from (2, 1) to (-1, -1), and from (2, 5) to (-1, 3). To reverse this translation, we need to move the triangle by the same amount but in the opposite direction.
The horizontal translation was from 2 to -1, so we need to move the x-coordinate in the opposite direction: -1 - (2 - (-1)) = -4. Similarly, the vertical translation was from 1 to -1, so we need to move the y-coordinate in the opposite direction: -1 - (1 - (-1)) = -3.
Therefore, the third vertex of the triangle before it was translated can be found by subtracting the reverse translation amounts from the translated position: (-2, 1) - (-4, -3) = (-2 - (-4), 1 - (-3)) = (2, 4).
So, the third vertex of the triangle before it was translated is located at (2, 4).