classify the triangle?

Question

Classify the triangle DEF with vertices D(1, 5), E(-3, 1), and F(-1, -3).
choices-
right
isosceles
scalene
equilateral

Answer 1

i believe it is scalene,

A right triangle would have a 90 degree angle in it
an isosceles would have 2 equal sides
and an equilateral would have all 3 sides equal,

if you draw up the points on a grid you will see that it doesn't meet any of these descriptions so I think it must be the only other option (Scalene)

Answer 2

We need to compute the lenght of the sides of the triangle:

m(DE) = Sqrt((-3-1)² + (1-5)²) = 4V2
m(DF) = Sqrt(((-1-1)² + (-3-5)²) =2V17
m(EF) = Sqrt(((-1+3)² + (-3-1)²) =2V5

(Note: "V" symbol means square root)

We also need to know if there is a right angle between two straight lines that passes for each pair of points.

slope DE = 1-5 / -3-1 = 1
slope DF = -3-5 / -1-1 = 4
slope EF = -2

product of slope DE x slope DF = (1)(4) = 4
product of slope DF x slope EF = (4)(-2) = -8
product of slope DE x slope EF = (1)(-2) = -2

None of these products is equal to -1 (condition of existence of right angle between two straight lines).

Hence (if my calculations are correct) Triangle is scalene (three sides are different lenght each other without right angle)

Good luck!

Answer 3

Pull out some paper and graph it...always easiest way to do it.