To rotate a shape 180º about the origin you have to switch the coordinates and invert their signs following the rule:
[tex](x,y)\to(-y,-x)[/tex]
First, you have to determine the coordinates of each vertex od ΔEFG
E(-3,-1)
F(2,1)
G(1,-4)
Next, apply the rule to the coordinates of each vertex to rotate the triangle:
[tex]E(-3,-1)\to E^{\prime}\lbrack-(-1),-(-3)\rbrack=E^{\prime}(1,3)[/tex][tex]F(2,1)\to F^{\prime}(-1,-2)[/tex][tex]G(1,-4)\to G^{\prime}\lbrack-(-4),-1\rbrack=G^{\prime}(4,-1)[/tex]
So, the coordinates of ΔE'F'G' are
E'(1,3)
F'(-1,-2)
G'(4,-1)
