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Answer :
Final answer:
The 90° rotation of triangle KLM about point K results in triangle K'L'M' having vertices K' = (0, 0), L' = (0, 3), and M' = (-4, 0).
Explanation:
The question involves the concept of geometric rotations, specifically the details about the result of a 90° rotation of triangle KLM around point K.
To perform this rotation, we need to take each vertex of the triangle and rotate it 90° around the origin point K.
When we rotate point L (3, 0), it will move to the position (0, 3), because a 90° rotation will switch the x and y coordinates and change the sign of the former x-coordinate.
Similarly, when we rotate point M (0, 4), it will move to the position (-4, 0). As a result, triangle K'L'M' will have vertices K' = K = (0, 0), L' = (0, 3), and M' = (-4, 0).
Therefore, the rotated triangle K'L'M' has its vertices at the specified coordinates after being rotated 90° about point K.
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