SOLUTION: Length of a Line Segment 20. The point A(x, 1) is 5 units from the point (2, 6). a) Find a possible value for x. b) Is this value the only solution? Explain. Thank you very muc

Question 188716: Length of a Line Segment
20. The point A(x, 1) is 5 units from the point (2, 6).
a) Find a possible value for x.
b) Is this value the only solution? Explain.
Thank you very much!!! pleaseeeeee
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, the distance between any two points

and

In this case,

is the point (x,1) and

is the point (2,6)

Now matching corresponding coordinates, we get , , , and

Start with the distance formula

Plug in (the given distance) , , , and (the given coordinates)

The goal now is to solve for "x":

Combine like terms.

Square -5 to get 25

Square both sides (to eliminate the square root)

Square 5 to get 25

Subtract 25 from both sides.

Combine like terms.

Rearrange the equation

Take the square root of both sides.

or Break up the "plus/minus" to form two equations.

or Take the square root of to get .

or Add to both sides.

or Combine like terms.

Remove the duplicate solution

--------------------------------------

Answer:

So the only solution is .

So the point (2,1) is 5 units from (2,6)

Note: if you plot the points on a coordinate plane and count the number of units one point is from another, you'll find that the two points are 5 units apart.
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