Given the following coordinates use distance formula to classify the triangle
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Given the following coordinates use distance formula to classify the triangle

[From: ] [author: ] [Date: 12-07-18] [Hit: ]
Angles: 90 at the vertex formed by the two equal sides, and 45 between the sides and the base.It is a right, isosceles triangle.......
A (-6, 3)
B (-2, -2)
C (3, 2)

Both sides AND angles, please!

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Begin by finding AB, AC and BC.

AB = B - A = (4, -5)
AC = C - A = (9, -1)
BC = C - B = (5, 4)

Thus we can tell that this is an isosceles triangle since AB and BC are of the same length.
They have length sqrt(4^2 + 5^2) = sqrt(41), while the length of the base is sqrt(9^2 + 1^2) = sqrt(82).

We are now interested in the angle formed; if we can find the angle between the two equal sides, we can extrapolate the other two angles since we know in an isoceles triangle they are equal. Using the inner/dot product:

(AB).(BC) = 4.5 - 5.4 = 0
Thus AB and BC are perpendicular and have angle 90 between them. Since the triangle angles add to 180, then the other two angles are both, say, θ, then 180 + 2θ = 90 which implies θ = 45.

So side lengths: sqrt(41) and base length sqrt(82).
Angles: 90 at the vertex formed by the two equal sides, and 45 between the sides and the base.

It is a right, isosceles triangle.
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