You need the distance formula to figure this out. The coordinates for point D are (-5, 1), the coordinates for point E are (-2, 3), and the coordinates for point F are (-3, -2). For the distance or length of DE, the formula looks like this: [tex]DE= \sqrt{(-5-(-2))^2+(1+3)^2} [/tex] which simplifies a bit down to [tex]DE= \sqrt{-3^2+4^2} [/tex] which is [tex]DE= \sqrt{9+16} [/tex] which of course is [tex]DE= \sqrt{25} [/tex] so DE = 25. Moving on to EF: [tex]EF= \sqrt{(-2-(-3))^2+(3-(-2))^2} [/tex] which simplifies to [tex]EF= \sqrt{1^2+5^2} [/tex] which is to say that [tex]EF= \sqrt{26} [/tex]. We do the same for FD: [tex]FD= \sqrt{(-5-(-3))^2+(1-(-2))^2} [/tex] which simplifies a bit to [tex]FD= \sqrt{4+9} [/tex] which is to say that the length of FD is [tex] \sqrt{13} [/tex]. None of the lengths of the sides are the same, so this is a scalene triangle. Last choice given above.
