You have to perform two transformations the first one is a 180º rotation with respect to the origin r(180º,O) and the second one is a translation of one unit left and 5 units up T(-1,5)
Given point A(8,-6)
To make a 180º rotation you have to invert the signs of both coordinates, following the rule:
[tex](x,y)\to(-x,-y)[/tex]For point A, the rotation is the following:
[tex]A(8,-6)\to A^{\prime}(-8,--6)=(-8,6)[/tex]Once you rotate the point, you have to perform the translation T(-1,5). The rule for the translation can be expressed as follows
[tex](x,y)\to(x-1,y+5)[/tex]So, the translation of point (-8,6) is:
[tex]A^{\prime}(-8,6)\to A^{\doubleprime}(-8-1,6+5)=(-9,11)[/tex]