SOLUTION: Triangle ABC with a vertices A(0,square root of 27) B(3,o) C(-3,0) Use the distance formula to classify the triangle by its sides.

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Question 182386: Triangle ABC with a vertices A(0,square root of 27) B(3,o) C(-3,0)
Use the distance formula to classify the triangle by its sides.
Answer by tvandenberg(45) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming by B(3,o) you meant (3,0)...
Distance is from a%5E2%2Bb%5E2=c%5E2 or c+=+sqrt%28a%5E2%2Bb%5E2%29
But, that means you need to know the a and the b. If you plotted this triangle, you'd see that AB = AC, as A is centered on the x-axis between B and C, and B and C are at the same y-value.
So, let's start with the easy one, BC = 6, since it is from -3 to 3.
So, you can either do AB or AC, I chose AB, for no real reason.
So, a and b, from the equation above are the x distance and y distance.
So, x-distance is (3-0) = 3
y-distance = sqrt%2827%29-0 = sqrt%2827%29
c+=+sqrt%28a%5E2%2Bb%5E2%29+=+sqrt%283%5E2%2B%28sqrt%2827%29%29%5E2%29+=+sqrt%2836%29+=+6
So the side are 6,6,6 which is an equilateral triangle.