find all points having an x-coordinate of 4 whose distance from the point (-4,2) is 10

Question

 find all points having an x-coordinate of 4 whose distance from the point (-4,2) is 10

Answer 1

Let (4, y) be such a point

 

So, we want to find y so that the distance from (-4,2) to (4,y) is 10

 

By the distance formula, √[(4-(-4))²+(y-2)²] = 10

 

Simplifying, we get:  √[64+y²-4y+4] = 10

 

Square both sides to obtain:  y²-4y+68 = 100

 

                                         y²-4y-32 = 0

 

                                         (y-8)(y+4) = 0

 

                                          y = 8 or y = -4

 

NOTE:  Since we squared both sides we need to check both values of y in the original equation to make sure that there are no extraneous solutions.  Doing this, we see that both values of y satisfy the original equation.  

Answer 2

Libby,

How many such points do you expect to find? I would start by sketching on a coordinate plane.  Label your point (-4,2), and a vertical line representing x=4.  Perhaps the line could be dotted.

 

Now imagine how you can fit a line segment of length 10 (this represents the distance), from x = -4 to x = 4.  How many ways can you do it?  With this diagram, a familiar figure (or figures) should pop out that will use some math that you know.  See if you can get somewhere with this information, and I will elaborate after you try if you need it.

 

Michael J

Athens GA