SOLUTION: Prove or disprove that Segment AB ~= Segment BC A (-2,0) B (10, -14) C (-4, -2)

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Question 1052239: Prove or disprove that Segment AB ~= Segment BC
A (-2,0)
B (10, -14)
C (-4, -2)
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
The length of the segment AB = sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29 where x2 = 10 ,
x1 = -2, y2 = -14 and y1 = 0
AB = sqrt%28%2810-%28-2%29%29%5E2%2B%28-14-0%29%5E2%29
AB = sqrt%28%2810%2B2%29%5E2%2B%28-14%29%5E2%29
AB = sqrt%28%2812%29%5E2%2B%28-14%29%5E2%29 = AB = sqrt%28%2812%29%5E2%2B%2814%29%5E2%29
The length of the segment BC = sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29 where
x2 = 10 , x1 = -4, y2 = -14 and y1 = -2
BC = sqrt%28%2810-%28-4%29%29%5E2%2B%28-14-%28-2%29%29%5E2%29
BC = sqrt%28%2810%2B4%29%5E2%2B%28-14%2B2%29%5E2%29
BC = sqrt%28%2814%29%5E2%2B%28-12%29%5E2%29
BC = sqrt%28%2814%29%5E2%2B%28-12%29%5E2%29 = BC = sqrt%28%2812%29%5E2%2B%2814%29%5E2%29
So we can see that the lengths of the two segments are the same at
sqrt%28%2812%29%5E2%2B%2814%29%5E2%29
Since the segments are the same length Segment AB ~= Segment BC