Question

the length of a line segment is $\sqrt{20}$ and its endpoints are (5,1) and (x,-3). What is the solution set for x?

Answer 1

To solve the length of a line, use the distance formula (which is also the pythagorean theorem). In this case, it's (5-x)^2 + (1+3)^2 = 20. 

Simplify that to (5-x)^2 + 16 = 20,
so (5-x)^2 = 4
So 5-x = 2 or -2,
so x = 3 or 7.