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