Step-by-step explanation & Answer:
For 8b, the distance between (2,a) and (5,1) is the square-root of the sum of squares of the difference in x and y directions, namely,
d^2 = ((2-5)^2+(a-1)^2 = 9+a^2-2a+1 ..............................(1)
We are given d^2=(sqrt(13)^2)= 13
so by substituting d^2=13, equation (1) becomes
a^2-2a+10=13
a^2-2a-3=0 [simplify]
(a-3)(a+1) = 0 [by factoring]
so a=3 or a=-1
If you have a different approach learned from school, please post what you would have done. It was not clear in the remark you posted.
Thank you!