9514 1404 393
Answer:
- DE ≈ 9.49, EF ≈ 8.06, FD ≈ 14.87
- obtuse scalene triangle
Step-by-step explanation:
For finding side lengths, it is convenient to work with the differences of the coordinates.
DE = E(-1, -3) -D(8, -6) = (-9, 3)
EF = F(-2, 5) -E(-1, -3) = (-1, 8)
FD = D(8, -6) -F(-2, 5) = (10, -11)
Then the lengths are ...
DE = √((-9)² +3²) = √90 = 3√10 ≈ 9.49
EF = √((-1)² +8²) = √65 ≈ 8.06
FD = √(10² +(-11)²) = √221 ≈ 14.87
The lengths are all different and the largest angle is obviously more than 90°, so the triangle is an obtuse scalene triangle.
