"Triangle LMN has L at (1,-1) and M at (2,3). Triangle L'M'N' has L' at (-1,-1) and M' is at (3,2). Describe the transformation."
This question is really tripping me up. I even tried putting it on a graph to solve it, but I just can't. PLEASE HELP!!!!!
What’s the answer
Sure, I'd be happy to help! Understanding transformations in geometry can sometimes be challenging, but with a step-by-step approach, it becomes more manageable.
To describe the transformation from Triangle LMN to Triangle L'M'N', we need to identify the specific type of transformation that occurred.
Here's how we can do it:
1. First, let's plot the given points on a coordinate plane. Triangle LMN has vertices L(1, -1) and M(2, 3), while Triangle L'M'N' has vertices L'(-1, -1) and M'(3, 2).
N'
( _______ )
( |
( |
(________ |
M' L')
N
( _______ )
( |
( ? |
(__________|
M L
2. To determine the transformation, we need to compare the corresponding sides and angles of the two triangles.
- Look at the positions of L and L'. The x-coordinate of L' is -1, whereas the x-coordinate of L is 1. This means that there has been a horizontal shift or translation of the triangle.
- Similarly, comparing the y-coordinates of L' and L (-1 and -1, respectively), we see that there has been no vertical shift or translation.
- Now, let's compare the positions of M and M'. The x-coordinate of M' is 3, whereas the x-coordinate of M is 2. This indicates a horizontal shift or translation as well.
- Finally, comparing the y-coordinates of M' and M (2 and 3, respectively), we can see that there has been a vertical shift or translation.
3. Combining the findings, we conclude that the transformation from Triangle LMN to Triangle L'M'N' involves both horizontal and vertical translations. L has shifted left by 2 units, M has shifted right by 1 unit, and both L and M have shifted up by 2 units.
Therefore, the transformation can be described as a translation to the left by 2 units and up by 2 units.
I hope this explanation clarifies the transformation for you! Let me know if you have any more questions.