Question 228655: Hello, my question is: If you were given three points on a coordinate plane and asked to determine if they were connected they formed:
a right triangle
a scalene triangle
an equilateral triangle
How could I explain this to a few students? I do have to use slope and distance formula here.
Thank you
Caroline
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Use the 3 pairs of points to find the slopes of the lines thru them.
If 2 of the slopes are negative inverses, they're perpendicular, --> a right triangle.
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If it's not a right triangle:
Find the distances between the point pairs.
If they're all equal, it's equilateral.
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If not:
Compare the squares of the sides.
If the square of the longest side is greater than the sum of squares of the other 2 sides, it's an obtuse triangle. o/w, it's scalene.
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