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hectictar

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Punkte9488
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 #1
avatar+9488 
+2

Alice is one the line  x = 4  ,  so the  x-coordinate of whatever point Alice is on is  4 .

Let's call the point that Alice is located  (4, y)  .

 

By the distance forumula...

 

the distance between  (4, y)  and  (2, 3)   =   (42)2+(y3)2

 

The problem tells us that the distance between  (4, y)  and  (2, 3)  is  √40 ,  so...

 

(42)2+(y3)2=40

                                                          Now let's solve this equation for  y .  First square both sides.

(42)2+(y3)2=40

                                                          Simplify  (42)2  to  4 .

4+(y3)2=40

                                                          Subtract  4  from both sides of the equation.

(y3)2=36

                                                          Take the ± square root of both sides.

y3=±36

 

y3=±6

                                                          Add  3  to both sides.

y=3±6

 

y=3+6ory=36 y=9ory=3

 

The possible y-coordinates of the point Alice at are  9  and  -3 .

 

The sum of the possible y-coordinates of the point Alice is at   =   9 + -3   =   6

 

To help check the answer, we can see on this graph that  (4, 9)  and  (4, -3) , the two possible points Alice is at, are the same distance away from  (2, 3) ...over 2 units and up or down  6  units.

19.08.2018
 #1
avatar+9488 
+2
07.07.2018