SOLUTION: Please help me with this problem: given the distance between (x,1) and (-2,5) is 2 sqrt (7) find the value of x.

Algebra ->  Length-and-distance -> SOLUTION: Please help me with this problem: given the distance between (x,1) and (-2,5) is 2 sqrt (7) find the value of x.       Log On


   



Question 981021: Please help me with this problem: given the distance between (x,1) and (-2,5) is 2 sqrt (7) find the value of x.
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the distance formula.
D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2
%282sqrt%287%29%29%5E2=%28x-%28-2%29%29%5E2%2B%281-5%29%5E2
28=%28x%2B2%29%5E2%2B16
%28x%2B2%29%5E2=12
x%2B2=0+%2B-+sqrt%2812%29
x=-2+%2B-+2sqrt%283%29
Two possible points
(-2%2B2sqrt%283%29,1) and (-2-2sqrt%283%29,1)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The first point is (x%5B1%5D,y%5B1%5D). The second point is (x%5B2%5D,y%5B2%5D).

Since the first point is (x,1), we can say (x%5B1%5D,y%5B1%5D) = (x,1)
So x%5B1%5D+=x, y%5B1%5D=1

Since the second point is (-2,5), we can also say (x%5B2%5D,y%5B2%5D) = (-2,5)
So x%5B2%5D=-2, y%5B2%5D=5.
Now use the distance formula:

d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29
since given d=2sqrt%287%29, x%5B1%5D+=x,y%5B1%5D=1,x%5B2%5D=-2, and y%5B2%5D=5, substitute these values

2sqrt%287%29=sqrt%28%28x-%28-2%29%29%5E2%2B%281-5%29%5E2%29
2sqrt%287%29=sqrt%28%28x%2B2%29%5E2%2B%28-4%29%5E2%29
2sqrt%287%29=sqrt%28%28x%2B2%29%5E2%2B16%29
2sqrt%287%29=sqrt%28x%5E2%2B4x%2B4%2B16%29.......square both sides
%282sqrt%287%29%29%5E2=%28sqrt%28x%5E2%2B4x%2B4%2B16%29%29%5E2
4%2A7=x%5E2%2B4x%2B20
28=x%5E2%2B4x%2B20
0=x%5E2%2B4x%2B20-28
0=x%5E2%2B4x-8...........use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-8%29+%29%29%2F%282%2A1%29+
x+=+%28-4+%2B-+sqrt%28+16%2B32+%29%29%2F2+
x+=+%28-4+%2B-+sqrt%28+48+%29%29%2F2+
x+=+%28-4+%2B-+sqrt%28+4%5E2%2A3+%29%29%2F2+
x+=+%28-cross%284%292+%2B-+cross%284%292sqrt%28+3+%29%29%2Fcross%282%29+
x+=+%28-2+%2B-+2sqrt%28+3+%29%29+
solutions:
x+=+-2+%2B+2sqrt%28+3+%29+
x+=+-2%281+-sqrt%28+3+%29%29+
or
x+=+-2+-+2sqrt%28+3+%29+
x+=+-2%281+%2Bsqrt%28+3+%29%29+

so, the first point is (x,1) could be:
(-2%281+-sqrt%28+3+%29%29,1)
or
(-2%281%2Bsqrt%283+%29%29,1)