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Answer :
Final answer:
Triangle KLM is congruent to triangle K' L' M' because a 90-degree rotation does not change the size or shape of the triangle, just its position. Thus, statement a) is correct.
The correct option is a.
Explanation:
The question pertains to the concept of congruency in triangles in the context of rotations in Mathematics. Here we have triangle KLM with vertices at K=(0,0), L=(3,0), M=(0,4) and a new triangle formed after a 90-degree rotation.
After a 90-degree rotation around point K, the triangle becomes K'=(0,0), L'=(-3, 0), M'=(0,-4). It is important to note that the size and shape of the triangle has not changed, only its position in the Cartesian plane. Therefore, the triangles KLM and K' L' M' are simply different orientations of the same triangle.
This implies that they are in fact congruent to each other, and the answer is statement a) Triangle KLM is congruent to triangle K' L' M'.
The correct option is a.
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