Triangle abc has been rotated 90° to create triangle def. using the image below, prove that lines bc and ef have the opposite and reciprocal slopes. you must show all of your work to receive credit. (10 points) triangles abc and def are shown. a is at 4, 2. b is at 4, 5. c is at 1, 2. d is at 2, negative 4. e is at 5, negative 4. f is at 2, negative 1. (10 points)

We have a lot of facts here. the first and most important fact is to calculate the slopes of the lines. if we have 2 points, indexed by the numbers 1 and 2, we have that their slope is . we can substitute now insted for the points 1 and 2 the points b and c. then we get that . similarly substituting for ef we get that the slope is -1. we have that 1=) and then that the product of the slopes is -1, as requested. hence, we have proven what was required.

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