Find the possible values of a, if the distance between the points is 5, and the coordinates are (1,1) and (4,a)

Question

I'm not quite sure how to do this one.. I've tried the distance and midpoint formula, but I'm confused.

I don't what to do with the (a-1)^2 part.

5= (4-0)^2 + (a-1)^2

5= 16 + (a-1)^2

Any help or can give me a site with detailed examples would greatly be appreciated. Thanks.

Answer 1

The formula for distance between two point is
d = √( (y2-y1)^2 + (x2-x1)^2

so

5 = √((a-1)^2 ++ (4-1)^2 )
square both sides
25 = (a-1)^2 = 9
16 = (a-1)^2
take √ of both sides
4 = ± (a-1)
a-1 = ±4
a = 5 or a= -3

Answer 2

Thank you Reiny!