Answer :

Luv2Teach
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.

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