Solution 1 :)
Let #k# be the scale factor, when #k# is negative, the "image" triangle is on the opposite side of the center of the dilation #O# (vertices are on opposite side of O from the preimage). Also note that the triangle has been rotated 180º.
In our case, #k=-2#, and the center of dilation is at the origin #O#, we can describe this transformation as a dilation of scale factor #k=+2# combined with a rotation of #180^@#.
1) Under a dilation centered at the origin with a scale factor #(k>0)#,
a point #A(x,y) -> A_1(kx,ky)#
see the pre-image and image-1 as shown in the figure above,
#=> P(-1,2) -> P_1(2xx(-1), " "2xx2)=color(red)(P_1(-2,4))#
#=> Q(-3,5) -> Q_1(2xx(-3), " "2xx5)=color(red)(Q_1(-6,10))#
#=> R(0,4) -> R_1(2xx0, " "2xx4)=color(red)(R_1(0,8)#
2) Under a rotation of #180^@# about the origin,
a point #A_1(kx,ky) -> A_2(-kx,-ky)#
see image-2 as shown in the figure,
#=> color(red)(P_1(-2,4)) -> color(blue)(P_2(2,-4))#
#=> color(red)(Q_1(-6,10)) -> color(blue)(Q_2(6,-10))#
#=> color(red)(R_1(0,8) -> color(blue)(R_2(0,-8)#
solution 2 :)
note that when #k < -1# , the image is larger, with a #180^@# rotation. The negative symbol indicates direction.
Formula for an enlargement with a negative scale factor #(k < -1)# and center at origin,
a point #A(x,y) = A'(-kx, -ky)#
#=> P(-1,2) -> P'(-2xx(-1), -2xx2)=color(blue)(P'(2,-4))#,
#=> Q(-3,5) -> Q'(-2xx(-3), -2xx5)=color(blue)(Q'(6,-10))#,
#=> R(0,4) -> P'(-2xx(0), -2xx4)=color(blue)(R'(0,-8))#
