Find x so the distance between (x,2) and (1,4) is square root 13.

x=5orx=−1

Explanation:

The distance between two points (x1,y1)and(x2,y2) is

D=√(x1−x2)2+(y1−y2)2 or

5=√(x−2)2+(3+1)2 squaring both sides we get ,

(x−2)2+(3+1)2=25orx2−4x+4+16−25=0 or

x2−4x−5=0orx2−5x+x−5=0 or

x(x−5)+1(x−5)=0or(x−5)(x+1)=0

∴x=5orx=−1

The point is (5,3)or(−1,3) [Ans]

table 3 represents a direct variation function. : )