Regarding Practice ppr 2

Qn 4
I dont understand the solutions for the first part when proving p(k+1) is true.

Qn 5
I cannot find the solutions! ><

Qn 11iii last part
It is asking to find the distance of XS, not YS.
So, the ans should be (3sqroot865)/17 which is given in the worksheet answer key.

Qn 12b
I cannot find the solutions too! ><

Please help me solve these problems asap, esp those who are in charge of the paper. thanks! ^^