Answer:
a=3
a= -19
Explanation:
(a+7i) (-8+4i) distance = sqrt(130)
distance = sqrt( (x2-x1) ^2 + (y2-y1) ^2)
fill in what we know
sqrt(130) =sqrt( (-8-a) ^2 + (4-7) ^2))
square each side
(130) =( (-8-a) ^2 + (4-7) ^2))
130 = (-8-a) ^2 + (-3) ^2)
130 = (-8-a) ^2 + 9
subtract 9 from each side
130 -9 = (-8-a) ^2 +9-9
121= (-8-a) ^2
take the square root of each side
sqrt(121) = sqrt( -8-a)^2)
remember to take the plus and minus when taking the square root
±11 =( -8-a)
11 = -8-a or -11 = -8-a
add 8 to each side
8+11 = 8-8-a or 8-11 = 8-8-a
19 = -a or -3 = -a
multiply by -1
a = -19 or a = 3