What is a correct classification of triangle DEF with vertices D(-3, -2), E(-2, 3), and F(1, 0)?
using an online triangle calculator
acute scalene
To classify a triangle, we usually look at the lengths of its sides and the measures of its angles. However, since we're given the coordinates of the vertices, we can use the distance formula to find the lengths of the sides.
The distance formula is given by:
d = √((x2-x1)^2 + (y2-y1)^2)
Let's calculate the lengths of the sides DE, EF, and FD.
1. DE:
Distance = √((-2 - (-3))^2 + (3 - (-2))^2)
= √((1)^2 + (5)^2)
= √(1 + 25)
= √26
2. EF:
Distance = √((1 - (-2))^2 + (0 - 3)^2)
= √((3)^2 + (-3)^2)
= √(9 + 9)
= √18 = 3√2
3. FD:
Distance = √((-3 - 1)^2 + (-2 - 0)^2)
= √((-4)^2 + (-2)^2)
= √(16 + 4)
= √20 = 2√5
Now that we have the lengths of the sides, let's analyze the triangle's classification based on its side lengths:
- If all sides have the same length, it is an equilateral triangle.
- If two sides have the same length and the third side is different, it is an isosceles triangle.
- If all sides have different lengths, it is a scalene triangle.
Now, we can see that the lengths of the sides of triangle DEF are √26, 3√2, and 2√5. Since none of the sides have the same length, it is classified as a scalene triangle.