The correct option is D 7
Given, the point P(2, -1) is equidistant from the points A(a, 7) and B(-3, a).
So, we have
PA=PB
⇒PA2=PB2
By using the distance formula, we have
(a−2)2+(7+1)2=(−3−2)2+(a+1)2
a2+4–4a+64=25+a2+1+2a
68–4a=26+2a
6a = 42
a = 7
Hence, the value of a is 7.