Question

Can someone help me on this

Answer 1

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: $DE= \sqrt{(-5-(-2))^2+(1+3)^2}$  which simplifies a bit down to $DE= \sqrt{-3^2+4^2}$  which is $DE= \sqrt{9+16}$  which of course is  $DE= \sqrt{25}$  so DE = 25.  Moving on to EF:  $EF= \sqrt{(-2-(-3))^2+(3-(-2))^2}$  which simplifies to  $EF= \sqrt{1^2+5^2}$  which is to say that  $EF= \sqrt{26}$.  We do the same for FD:  $FD= \sqrt{(-5-(-3))^2+(1-(-2))^2}$  which simplifies a bit to  $FD= \sqrt{4+9}$  which is to say that the length of FD is $\sqrt{13}$.  None of the lengths of the sides are the same, so this is a scalene triangle.  Last choice given above.