The vertices of △DEF are D(1, 19), E(16, −1), and F(−8, −8). What type of triangle is △DEF?

Question

1. A.
2. right
3. 
   
4. B.
5. equilateral
6. 
   
7. C.
8. isosceles
9. 
   
10. D.
11. scalene

Answer 1

Triangles can be classified by sides and angles.

The distance formula can be used to find the length of three sides. If no lengths are equal its scalene, if 2 or more sides are equal its isosceles, if 3 sides are equal it is equilateral.

The distance formula is the square root of [(x1-x2)² + (y1-y2)²]

Next we need to see if there is a right angle in the triangle which would make it a right triangle. It is a right triangle if two of the sides are perpendicular. The sides are perpendicular if their slopes are opposite reciprocals. So use the slope formula to find the slopes of each side. If any two slopes are opposite reciprocals than it is a right triangle.