Problem with distance formula.

The coordinates I'm given for a cartesian plane are (1,y) and (3,2). I'm supposed to find an answer for y that gives a hypotenuse of 4.

In the book it says "We obtain two answers: (1, 2 + 2 √3) and (1, 2 − 2 √3). The reader is encouraged to think about why there are two answers."

I'm lost on how this results in negative and positive answers. I'm unfamiliar or need refreshing with this concept and don't know where to begin. I just posted this to save time. There's an image below of the graphics from the book. Any help would be appreciated.


Attachment 19082

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Originally Posted by MellowViper

The coordinates I'm given for a cartesian plane are (1,y) and (3,2). I'm supposed to find an answer for y that gives a hypotenuse of 4.

In the book it says "We obtain two answers: (1, 2 + 2 √3) and (1, 2 − 2 √3). The reader is encouraged to think about why there are two answers."

I'm lost on how this results in negative and positive answers. I'm unfamiliar or need refreshing with this concept and don't know where to begin. I just posted this to save time. There's an image below of the graphics from the book. Any help would be appreciated.


Attachment 19082

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Start by plotting the point (3, 2) and drawing the line x = 1. It should be clear why there are two points on the line that are distance of 4 units from (3, 2).

The working given that leads to the two solutions is extremely clear. What part of it do you not understand?

Oh duh. the positive ordinate just creates a mirror image of the bottom triangle that's formed with the negative ordinate. Thanks.

Purely geometrically, draw the vertical line x= 1 and a circle with center at (3, 2) and radius 4. Since the line x= 1 is only distance 3-1= 2 from that point, the line passes through the interior of the circle and must cross the circle twice.

That makes even more sense.